Routing Area Working Group                                 A. Atlas, Ed.
Internet-Draft                                        M. Konstantynowicz
Intended status: Informational                          Juniper Networks
Expires: January 5, 2012                                       G. Enyedi
                                                              A. Csaszar
                                                                R. White
                                                                M. Shand
                                                           Cisco Systems
                                                            July 4, 2011

An Architecture for IP/LDP Fast-Reroute Using Maximally Redundant Trees


   As IP and LDP Fast-Reroute are increasingly deployed, the coverage
   limitations of Loop-Free Alternates are seen as a problem that
   requires a straightforward and consistent solution for IP and LDP,
   for unicast and multicast.  This draft describes an architecture
   based on redundant backup trees where a single failure can cut a
   point-of-local-repair from the destination only on one of the pair of
   redundant trees.

   One innovative algorithm to compute such topologies is maximally
   disjoint backup trees.  Each router can compute its next-hops for
   each pair of maximally disjoint trees rooted at each node in the IGP
   area with computational complexity similar to that required by

   The additional state, address and computation requirements are
   believed to be significantly less than the Not-Via architecture

Status of this Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference

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   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on January 5, 2012.

Copyright Notice

   Copyright (c) 2011 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   ( in effect on the date of
   publication of this document.  Please review these documents
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   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  4
     1.1.  Goals for Extending IP Fast-Reroute coverage beyond LFA  .  4
   2.  Maximally Redundant Trees (MRT)  . . . . . . . . . . . . . . .  5
     2.1.  Redundant Trees Overview . . . . . . . . . . . . . . . . .  5
   3.  Maximally Redundant Trees (MRT) and Fast-Reroute . . . . . . .  6
     3.1.  Multi-homed Prefixes . . . . . . . . . . . . . . . . . . .  7
     3.2.  Unicast Forwarding with MRT Fast-Reroute . . . . . . . . .  8
       3.2.1.  IP Unicast Forwarding  . . . . . . . . . . . . . . . .  8  Protocol Extensions and Considerations: OSPF
                   and ISIS . . . . . . . . . . . . . . . . . . . . .  9
       3.2.2.  LDP Unicast Forwarding . . . . . . . . . . . . . . . .  9  Protocol Extensions and Considerations: LDP  . . . 10
     3.3.  Multicast Forwarding with MRT Fast-Reroute . . . . . . . . 10
       3.3.1.  Tunneled?  Yes . . . . . . . . . . . . . . . . . . . . 11
       3.3.2.  PIM Forwarding . . . . . . . . . . . . . . . . . . . . 11  Protocol Extensions and Considerations: PIM  . . . 12
       3.3.3.  mLDP Forwarding  . . . . . . . . . . . . . . . . . . . 12
       3.3.4.  Live-Live Multicast  . . . . . . . . . . . . . . . . . 13
     3.4.  MRT Algorithm Open Issues  . . . . . . . . . . . . . . . . 13
       3.4.1.  SRLG Protection  . . . . . . . . . . . . . . . . . . . 14
       3.4.2.  Common Computation . . . . . . . . . . . . . . . . . . 14
   4.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 14
   5.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 14
   6.  Security Considerations  . . . . . . . . . . . . . . . . . . . 14
   7.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 15
     7.1.  Normative References . . . . . . . . . . . . . . . . . . . 15
     7.2.  Informative References . . . . . . . . . . . . . . . . . . 15
   Appendix A.  Computing Maximally Redundant Trees . . . . . . . . . 16
     A.1.  Simple pair of maximally redundant trees in
           2-connected networks . . . . . . . . . . . . . . . . . . . 16
     A.2.  Non-2-connected networks . . . . . . . . . . . . . . . . . 18
     A.3.  Finding maximally redundant trees in distributed
           environment  . . . . . . . . . . . . . . . . . . . . . . . 20
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 20

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1.  Introduction

   There is still work required to completely provide IP and LDP Fast-
   Reroute[RFC5714] for unicast and multicast traffic.  This draft
   proposes an architecture to provide 100% coverage.

   Loop-free alternates (LFAs)[RFC5286] provide a useful mechanism for
   link and node protection but getting complete coverage is quite hard.
   [LFARevisited] defines sufficient conditions to determine if a
   network provides link-protecting LFAs and also proves that augmenting
   a network to provide better coverage is NP-hard.
   [I-D.ietf-rtgwg-lfa-applicability] discusses the applicability of LFA
   to different topologies with a focus on common PoP architectures.

   While Not-Via [I-D.ietf-rtgwg-ipfrr-notvia-addresses] is defined as
   an architecture, in practice, it has proved too complicated and
   stateful to spark substantial interest in implementation or
   deployment.  Academic implementations [LightweightNotVia] exist and
   have found the address management complexity high (but no
   standardization has been done to reduce this).

   A different approach is needed and that is what is described here.
   It is based on the idea of using disjoint backup topologies as
   realized by Maximally Redundant Trees (described in
   [LightweightNotVia]); the general architecture could also apply to
   future improved redundant tree algorithms.

1.1.  Goals for Extending IP Fast-Reroute coverage beyond LFA

   Any scheme proposed for extending IPFRR network topology coverage
   beyond LFA, apart from attaining basic IPFRR properties, should also
   aim to achieve the following usability goals:

   o  ensure maximum physically feasible link and node disjointness
      regardless of topology,

   o  automatically compute backup next-hops based on the topology
      information distributed by link-state IGP,

   o  do not require any signaling in the case of failure and use pre-
      programmed backup next-hops for forwarding,

   o  introduce minimal amount of additional addressing and state on

   o  enable gradual introduction of the new scheme and backward

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   o  and do not impose requirements for external computation.

2.  Maximally Redundant Trees (MRT)

   In the last few years, there's been substantial research on how to
   compute and use redundant trees.  Redundant trees are directed
   spanning trees that provide disjoint paths towards their common root.
   These redundant trees only exist and provide link protection if the
   network is 2-edge-connected and node protection if the network is
   2-vertex-connected.  Such connectiveness may not be the case in real
   networks, either due to architecture or due to a previous failure.
   The work on maximally redundant trees has added three useful pieces
   that make them ready for use in a real network.

   o  Computable when network isn't 2-edge or 2-vertex connected: The
      maximally redundant trees are computed so that only the cut-edges
      or cut-vertices are shared between the multiple trees.

   o  Algorithm is based on a common network topology database.  No
      messaging as has been suggested in other work is necessary.

   o  An algorithm [MRTLinear] is given that allows a router to compute
      its next-hops on each pair of maximally redundant trees to each
      node in the network in O( e ) time - or O(e + n log n), if
      Dijkstra is used instead of BFS.

   There is, of course, significantly more in the literature related to
   redundant trees and even fast-reroute, but the formulation of the
   Maximally Redundant Trees (MRT) algorithm makes it very well suited
   to use in routers.

   A known disadvantage of MRT, and redundant trees in general, is that
   the trees do not necessarily provide shortest detour paths.  The use
   of SPF in tree-building and some heuristics can improve this, but the
   length of the alternate paths is topology-dependent.  Providing
   shortest detour paths would require failure-specific detour paths
   such as in [I-D.ietf-rtgwg-ipfrr-notvia-addresses], but the state-
   reduction advantage of MRT lies in the detour being established per
   destination (root) instead of per destination AND per failure.

   A simple but not optimal way of computing maximally redundant trees
   is described in Appendix A.

2.1.  Redundant Trees Overview

   In graph theory, a pair of maximally redundant trees are a pair of
   directed spanning trees of an directed graph with a common root node

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   (this root can be any node of the graph), such that the two paths
   along the two trees to the root from any other node are as edge-
   disjoint and as vertex-disjoint as it is possible.  It is known that
   such trees can be found in any connected networks for any selected
   root.  A pair of trees for the graph depicted in Figure 1 is shown in
   Figure 2 considering "r" as the root.

                       e---d      i
                      /   / \    /|
                     r---c   f--g |
                      \   \ /    \|
                       a---b      j

                    Figure 1: A non-2-connected network

              e---d      i         e---d      i
             /          /|            / \     |
            r   c   f--g |       r---c   f--g |
             \   \ /     |            \      \|
              a---b      j         a---b      j

      Figure 2: The two maximally redundant trees rooted at node "r".

   The two paths along the two trees to a given root of a 2-connected
   graph are node-disjoint, while in any non-2-connected graph, only the
   cut-vertices and cut-edges can be contained by both of the paths.  As
   an example consider the trees depicted in Figure 2.  Here, the two
   paths from e.g. node "b" to "r" are node-disjoint (since there are
   such two paths), and the two paths from e.g. node "i" to "r" have
   only node "f" and "g" and link "f-g" in common.

3.  Maximally Redundant Trees (MRT) and Fast-Reroute

   In normal IGP routing, each router has its shortest-path-tree to all
   destinations.  From the perspective of a particular destination, D,
   this looks like a reverse SPT (rSPT).  To use maximally redundant
   trees, in addition, each destination D has two maximally redundant
   trees associated with it; by convention these will be called the red
   and blue redundant trees.

   Redundant trees are practical to maintain redundancy even after a
   single link or node failure.  If a pair of maximally redundant trees
   is computed rooted at each node, all the nodes remain reachable along
   one of the trees in the case of a single link or node failure.

   When there is a link or node failure affecting the rSPT, each node

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   will still have a path via one of the redundant trees to reach the
   destination D. Consider a simple 5-node ring (S--A--B--D--C--S), with
   traffic sent from sources S and C to destination D. In this case, if
   the link C->D fails, then C can forward traffic along the blue
   redundant tree to reach D. Of course, if the link S->C fails, then S
   can simply use its LFA of A.

   In a failure free network, packets are forwarded along the shortest
   path tree as done today.  However, if forwarding the packet fails at
   a node, the router detecting the failure locally reroutes the packet
   along the blue MRT.  If forwarding the packet along the blue MRT
   fails again, the packet is forwarded along the red MRT.  If there is
   only a single link or node failure, the packet must get to the root
   along either of the trees.  Therefore if forwarding along the red MRT
   fails, either multiple failures occurred, or the single failure split
   the network into two, and packets must be dropped.

   The above logic gives the following basic rules for unicast use of
   maximally redundant trees and fast-reroute when failure of the
   primary is detected are:

   1.  If there is an node-protecting LFA, use it.

   2.  Otherwise, if only link-protection is acceptable and there is a
       link-protecting LFA, use it.

   3.  Otherwise, if the blue MRT next-hop shouldn't fail with the
       primary, send traffic along the blue MRT next-hop.

   4.  Otherwise, if the red MRT next-hop shouldn't fail with the
       primary, send traffic along the red MRT next-hop.

   5.  If traffic is received on the blue redundant tree and the
       appropriate next-hop is not available, then send the traffic on
       the red redundant tree.

   6.  If traffic is received on the red redundant tree and the
       appropriate next-hop is not available, discard it.

3.1.  Multi-homed Prefixes

   One advantage of LFAs that would be good to preserve is the ability
   to protect multi-homed prefixes against ABR failure.  For instance,
   if a prefix from the backbone is available via both ABR A and ABR B,
   if A fails, then the traffic should be redirected to B. This can also
   be done for backups via MRT.

   If there exist multiple multi-homed prefixes that share the same

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   connectivity and the difference in metrics to those routers, then a
   single proxy-node can be used to represent the set.  In addition to
   computing the pair of MRTs associated with each router destination D
   in the area, a pair of MRTs can be computed for each such proxy-node
   to fully protect against ABR failure.

3.2.  Unicast Forwarding with MRT Fast-Reroute

   With LFA, there is no need to tunnel unicast traffic, whether IP or
   LDP.  The traffic is simply sent to an alternate.  The behavior with
   MRT Fast-Reroute is different depending upon whether IP or LDP
   unicast traffic is considered.

   Logically, one could use the same IP address or LDP FEC and then also
   use 2 bits to express the topology to use.  The topology options are
   (00) IGP/SPT, (01) blue MRT, (10) red MRT.  Unfortunately, there just
   aren't 2 spare bits available in the IPv4 or IPv6 header.  This has
   different consequences for IP and LDP because LDP can just add a
   topology label on top or take 2 spare bits from the label space.

3.2.1.  IP Unicast Forwarding

   For IP, there is no currently practical alternative except tunneling.
   The tunnel egress can be the original destination in the area, the
   next-next-hop, etc..  If the tunnel egress is the original
   destination router, then the traffic remains on the redundant tree
   with sub-optimal routing.  If the tunnel egress is the next-next-hop,
   then protection of multi-homed prefixes and node-failure for ABRs is
   not available.

   In either case, each router that supports MRT fast-reroute would need
   to announce two additional loopback addresses and their associated
   MRT color.  Those addresses are used as destination addresses for
   MRT-blue and MRT-red IP tunnels respectively.  They allow the transit
   nodes to identify the traffic as being forwarded along either MRT-
   blue or MRT-red tree topology to reach the tunnel destination.
   Announcements of these two additional loopback addresses per router
   with their MRT color requires IGP extensions.

   IP packets could be tunneled via LDP.  This has the advantage that
   more routers can do line-rate encapsulation and decapsulation.  If
   tunneled via LDP, naturally one of the LDP unicast forwarding options
   would need to be used.  It would be possible to use just a LDP
   Topology-Identifier label on top of the IP packet; if done, this
   would avoid any need to allocate or signal additional IP addreses and
   is particularly interesting for multi-homed prefixes.

   For proxy-nodes associated with one or more multi-homed prefixes, the

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   problem is harder because there is no router associated with the
   proxy-node, so its loopbacks can't be known or used.  In this case,
   each router attached to the proxy-node could announce two common IP
   addresses with their associated MRT colors.  This would require
   configuration as well as the previously mentioned IGP extensions.
   Similarly, in the LDP case, two additional FEC bindings could be
   announced.  Protocol Extensions and Considerations: OSPF and ISIS

   This captures an initial understanding of what may need to be

   o  Capabilities: Does a router support MRT?  Does the router do MRT
      tunneling with LDP or IP or GRE or...?

   o  Topology Association: A router needs to advertise a loopback and
      associate it with an MRT whether blue or red.  Additional
      flexibility for future uses would be good.

   o  Proxy-nodes for Multi-homed Prefixes: We need a way to advertise
      common addresses with MRT for multi-homed prefixes' proxy-nodes.
      Currently, those proxy-nodes aren't named or considered.

   o  Algorithm-specific Commonalities: In specifying the exact details
      for a common algorithm, there may be tie-breakers that are better
      done based on configuration than just using Router ID.

   As with LFA, it is expected that OSPF Virtual Links will not be

3.2.2.  LDP Unicast Forwarding

   For LDP, it is very desirable to avoid tunneling because, for at
   least node protection, this requires knowledge of remote LDP label
   mappings.  There are two different mechanisms that could be used.

   1.  Create Topology-Identification Labels: Use the label-stacking
       ability of MPLS and specify only two additional labels - one for
       each associated MRT color - by a new FEC type.  When sending a
       packet onto an MTR, first swap the LDP label and then push the
       topology-identification label for that MTR color.  When receiving
       a packet with a topology-identification label, pop it and use it
       to guide the next-hop selection in combination with the next
       label in the stack; then swap the remaining label, if
       appropriate, and push the topology-identification label for the
       next-hop.  This has minimal usage of additional labels, memory
       and LDP communication.  It does increase the size of packets and

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       the complexity of the required label operations and look-ups.

   2.  Encode Topology in Labels: In addition to sending a single label
       for a FEC, a router would provide two additional labels with
       their associated MRT colors.  This is simple, but reduces the
       label space for other uses.  It also increases the memory to
       store the labels and the communication required by LDP.

   Note that with LDP unicast forwarding, regardless of whether
   topology-identification label or encoding topology in label is used,
   no additional loopbacks per router are required as are required in
   the IP unicast forwarding case.  This is because LDP labels are used
   on a hop-by-hop basis to identify MRT-blue and MRT-red forwarding
   trees.  Protocol Extensions and Considerations: LDP

   This captures an initial understanding of what may need to be

   1.  Topology-Identification Labels: Define a new FEC type that
       describes the topology for MRT and the associated MRT color.

   2.  Specify Topology in Label: When sending a Label Mapping, have the
       ability to send a Label TLV and multiple Topology-Label TLVs.
       The Topology-Label TLV would specify MRT and the associated MRT

3.3.  Multicast Forwarding with MRT Fast-Reroute

   There are several basic issues with doing Fast-Reroute for multicast
   traffic, whether the alternates used are LFA or MRT.  They are given

   1.  The Point-of-Local-Repair (PLR) does not know the set of next-
       next-hops in the multicast tree.

   2.  For mLDP, the PLR does not know the appropriate labels to use for
       the next-next-hops in the multicast tree.

   3.  The Merge Point (MP) does not know upon what interface to expect
       backup traffic.  For LFAs, this is a particular issue since the
       LFA selected by a PLR is known only to that PLR.

   There are also issues about how to manage traffic.

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   a.  When should the PLR stop sending traffic on the alternate?  Based
       upon a configurable time-out is the most general answer.  For
       PIM, an explicit Withdraw or Backup Withdraw could be sent, but
       they could always be lost and are not reliable.  For mLDP, even
       if the PLR is known, for node-protection, there is no targeted
       LDP session and so no way for the MP to explicitly withdraw the
       label that was implicitly learned by the PLR.

   b.  Can anything be done about traffic missed due to different
       latencies along new primary and alternate/old primary trees?  If
       a router is willing and able to examine traffic from both the
       alternate and new primary, perhaps the full set of packets could
       be assured.  This requires more investigation, but such an option
       would be at most optional.  A router could also continue to
       accept traffic from both the old alternate and the new primary
       for a period longer than the expected difference in latency, but
       this comes with a possible doubling of traffic during that

3.3.1.  Tunneled?  Yes

   The disadvantages of tunneling unicast traffic do not fully translate
   to those for multicast.  With MRT fast-reroute, IP unicast traffic is
   tunneled.  With mLDP, in the suggested extensions (later), along with
   learning the next-next-hops on the multicast tree, the associated
   labels can be learned so there is no need for targeted sessions.

   If multicast traffic is not tunneled along the alternates, then there
   is the question of what happens when unencapsulated backup traffic
   intersects the normal multicast tree before reaching the MPs.
   Resolving this is likely to introduce significant complexity and
   state into the routers, with the only gain being the avoidance of a

   Therefore, tunneling for IP and mLDP multicast traffic along the
   selected alternates is required.  This means all replication is done
   by the PLR.

3.3.2.  PIM Forwarding

   For node-protection, the merge points would be the next-next-hops in
   the tree.  For a PLR to learn them, additional PIM Join Attributes
   [I-D.ietf-pim-mtid] need to be defined to specify the set of next-
   hops from which the sending node has received Joins.  For link-
   protection, of course a PLR knows the routers that have sent it

   An MP must know the interface that alternate traffic should be

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   accepted from.  To do this, a new Upstream Backup Join would be added
   to PIM.  This Upstream Backup Join would be sent by the PLR to MPs.
   If the PLR has selected an LFA for a MP, then the PLR tunnels the
   Upstream Backup Join to the MP via the LFA.  If the PLR will use MRT,
   then the PLR must send two Upstream Backup Joins - one transmited via
   the blue MRT and one transmited via the red MRT; these will also be
   tunneled via LDP or IP as is configured in the network.

   The Upstream Backup Join will specify the PLR, the MP, the (S, G),
   and the alternate details (e.g.  LFA with neighbor address, blue MRT,
   red MRT).  If desired, the alternate topology could be used to verify
   the incoming interface appropriately via a tree-appropriate RPF
   check.  Upon receiving the Upstream Backup Join, the MP will accept
   specified multicast traffic from the LFA backup neighbour, blue or
   red MRT respectively.  Protocol Extensions and Considerations: PIM

   This captures an initial understanding of what may need to be
   specified.  This is focusing on PIM Sparse mode.

   o  Capabilities: New Hello Option Capabilities to indicate the
      ability to understand the new Join Attributes and Upstream Backup

   o  Next-Hops: Need a new Join Attribute[I-D.ietf-pim-mtid] to send
      the next-hops to the PLR.  This list could be updated and sent
      upstream every time it changes.

   o  Upstream Backup Join

3.3.3.  mLDP Forwarding

   As in PIM, in mLDP[I-D.ietf-mpls-ldp-p2mp] a mechanism must be added
   so that the PLR can learn the next-next-hops.  The PLR also needs to
   learn the associated label-bindings.  This can be done via a new P2MP
   Child Data Object.  This object would include the primary loopback of
   an LSR that has provided labels for the FEC to the sending LSR along
   with the label specified.  Multiple P2MP Child Data Objects could be
   included in a P2MP Label Mapping; only those specified in the most
   recent P2MP Label Mapping should be stored and used.

   This will provide the PLR with the MPs and their associated labels.
   The MPs will accept traffic received with that label from any
   interface, so no signaling is required before the alternates are

   Traffic sent out each alternate will be tunneled with a destination

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   of the MP.

3.3.4.  Live-Live Multicast

   In MoFRR [I-D.karan-mofrr], the idea of joining both a primary and a
   secondary tree is introduced with the requirement that the primary
   and secondary trees be link and node disjoint.  This works well for
   networks where there are dual-planes, as explained in
   [I-D.karan-mofrr].  For other networks, it may still be desirable to
   have two disjoint multicast trees and allow a receiver to join both
   and make its own decision about what to do.

   MRT allows this, but would require minor extensions to PIM or mLDP.
   The pair of maximally redundant trees is rooted at the multicast
   group source S. IF asymmetric link costs aren't a concern, then the
   same set of next-hops (previous-hops in this case) could be used as
   is used for MRT fast-reroute.  The extension to PIM would be to
   specify which MRT tree is being joined - so instead of specifying
   join(S,G), it would specify join(S,G, MRT red) or join(S,G, MRT
   blue).  Similarly, a new P2MP FEC with Tree Identifier Element would
   need to be defined; it would include the topology to be used which
   could be IGP, MRT red, or MRT blue.

   The receiver would still need to detect failures and handle traffic
   discarding as is specified in [I-D.karan-mofrr].

3.4.  MRT Algorithm Open Issues

   The MTR algorithm as given in [MRTLinear] handles most of the issues
   that occur in real networks, but there are a few aspects that need to
   be considered and factored in.

   o  Broadcast Interfaces: While a broadcast interface can simply be
      represented as a pseudo-node in the graph, the rules for handling
      it given that there is a requirement to provide node-protection as
      well as link-protection need to be defined.

   o  Parallel Links: It is quite common to have parallel links in a
      real network.  In the case where node-disjoint paths are possible,
      the parallel links just introduce the possibility of multiple
      next-hops along the MTR.  In the case where node-disjoint paths
      aren't possible, having the ability to use parallel links is

   o  Improved Paths in MTRs: In the tree-building, it should be
      straightforward to use SPF instead of BFS.  There are additional
      heuristics in the Finding Multiple Maximally Redundant Trees in
      Linear Time paper that should be evaluated for realistic benefits.

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   o  Asymmetric Link Costs: The tree-building must consider that links
      may have asymmetric costs.

   o  Administratively Unavailable Links and Nodes: With the standard
      need to avoid a flag day, not all routers may participate in MTR
      and those that aren't must not be used in an MTR.  Additionally,
      links can be overloaded or administratively specified as not
      available just as is considered with LFA.  Such links may not be
      used in the MTR.

   o  ECMP: Consider the ability to use multiple equal-cost paths in
      building the MRT to get additional capacity along the MRT.

3.4.1.  SRLG Protection

   As shown in Appendix A, a straightforward way to build two redundant
   trees involves taking a link from a ready node to a non-ready node to
   provide one path and then determining the shortest-path back to a
   ready node that doesn't include that ready node.  Creating similar
   redundancy with arbitrarily placed Shared-Risk Link Groups is still a
   challenging open problem.

3.4.2.  Common Computation

   In the MTR algorithm, there are some places where decisions are made
   as to which link to use next, which neighbor to consider, etc.  The
   exact rules to follow and a detailed algorithm with example need to
   be provided.  Ideally, there would be reference pseudo-code.

4.  Acknowledgements

   The authors would like to thank Hannes Gredler, Robert Kebler, Ted
   Qian, Kishore Tiruveedhula, Santosh Esale, Nitin Bahadur, Harish
   Sitaraman and Raveendra Torvi for their suggestions and review.

5.  IANA Considerations

   This doument includes no request to IANA.

6.  Security Considerations

   This architecture is not currently believed to introduce new security

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7.  References

7.1.  Normative References

              Minei, I., Wijnands, I., Kompella, K., and B. Thomas,
              "Label Distribution Protocol Extensions for Point-to-
              Multipoint and Multipoint-to-Multipoint Label Switched
              Paths", draft-ietf-mpls-ldp-p2mp-14 (work in progress),
              June 2011.

              Cai, Y. and H. Ou, "PIM Multi-Topology ID (MT-ID) Join
              Attribute", draft-ietf-pim-mtid-08 (work in progress),
              June 2011.

              Karan, A., Filsfils, C., Farinacci, D., Decraene, B.,
              Leymann, N., and T. Telkamp, "Multicast only Fast Re-
              Route", draft-karan-mofrr-01 (work in progress),
              March 2011.

   [RFC5286]  Atlas, A. and A. Zinin, "Basic Specification for IP Fast
              Reroute: Loop-Free Alternates", RFC 5286, September 2008.

   [RFC5714]  Shand, M. and S. Bryant, "IP Fast Reroute Framework",
              RFC 5714, January 2010.

7.2.  Informative References

              Shand, M., Bryant, S., and S. Previdi, "IP Fast Reroute
              Using Not-via Addresses",
              draft-ietf-rtgwg-ipfrr-notvia-addresses-07 (work in
              progress), April 2011.

              Filsfils, C., Francois, P., Shand, M., Decraene, B.,
              Uttaro, J., Leymann, N., and M. Horneffer, "LFA
              applicability in SP networks",
              draft-ietf-rtgwg-lfa-applicability-02 (work in progress),
              May 2011.

              Retvari, G., Tapolcai, J., Enyedi, G., and A. Csaszar, "IP
              Fast ReRoute: Loop Free Alternates Revisited", Proceedings
              of IEEE INFOCOM , 2011, <

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              Enyedi, G., Retvari, G., Szilagyi, P., and A. Csaszar, "IP
              Fast ReRoute: Lightweight Not-Via without Additional
              Addresses", Proceedings of IEEE INFOCOM , 2009,

              Enyedi, G., Retvari, G., and A. Csaszar, "On Finding
              Maximally Redundant Trees in Strictly Linear Time", IEEE
              Symposium on Computers and Comunications (ISCC) , 2009,

   [Maintaining Colored Trees]
              "Maintaining colored trees for disjoint multipath routing
              under node failures", IEEE/AC Transactions on
              Networking vol. 17, no. 1, pp. 346-359, 2009, <http://

Appendix A.  Computing Maximally Redundant Trees

   This is possible but not optimal way to compute maximally redundant
   trees.  It is included to provide some intuition about how the
   maximally redundant trees are built.

   In Appendix A.1, we describe how to handle a network that is
   2-connected.  Then that is assumption is relaxed and finally how to
   handle distributed computation to obtain the same trees is given.

A.1.  Simple pair of maximally redundant trees in 2-connected networks

   Finding a simple pair of maximally redundant trees in a 2-connected
   network is straightforward.  We call a node "ready", if it was
   already added to the trees.  Initially, the only ready node is the
   common root (node r in the sequel).

   When we have at least one node x in the network, which is not ready,
   find two node-disjoint paths from x either to r or to two distinct
   ready nodes.  Since the network is 2-connected, there are always two
   node-disjoint paths from x to r.  It is possible that one or both of
   these paths reaches another ready node sooner than r, in which case
   we have the two node-disjoint paths to distinct nodes.  Combining the
   directed links of these paths makes up an *ear*.

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     Figure 3: An *ear* connected to node x and y (x and y are ready).

   Let x and y be the two ready endpoints of an ear, and first suppose
   that they are different nodes and none of them is r.  Note that both
   x and y are in the two trees (since they are "ready") and if x is an
   ancestor of y in the first tree (x is on the path from y to r), then
   x cannot be the ancestor of y along the second tree at the same time.
   Thus, it is safe to connect the nodes of the freshly found ear to x
   in the first tree and to y in the second tree, if either x is an
   ancestor of y in the first tree, or y is an ancestor of x in the
   second tree.  Considering the example in Figure 3, this means that
   links d-c-b-a-x should be added to the first tree, and a-b-c-d-y
   should be added to the second one.

   In the case, when either x=r or y=r or when neither x is an ancestor
   of y nor y is an ancestor of x in any of the trees, the endpoints are
   not firmly bound to one of the trees, it is only important to put the
   links to one endpoint in one of the trees and put the links towards
   the other endpoint to the other tree.  In our example this means that
   either d-c-b-a-x or a-b-c-d-y could be added to the first tree.
   Naturally, then the other endpoint must be selected for the second

   In some cases, we need to construct such (maximally) redundant trees,
   where there is only one edge entering to the root on one of the
   trees.  This makes the root a leaf in that tree.  To achieve this, we
   can add the ear to the second tree through r only if both endpoints
   are r.  Moreover, we need to select an ear with different endpoints
   when it is possible (it is always possible except for the first ear,
   if the network is 2-connected).

   Finding an ear is relatively simple and can be done in different
   ways.  Probably the simplest way is to find a ready node q (q is not
   the root) with a non-ready neighbor w, (virtually) remove q from the
   topology, and to find a path from w to r; since the network is 2-
   connected, such a path either reaches r, or reach another ready node.
   Moreover, when only r is ready such a node q does not exist, so we
   select one of r's neighbors as w, and remove not r but the link
   between them.

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                            /   / \
                           r---c   f
                            \   \ /

                      Figure 4: A 2-connected network

                   e---d              e---d
                  /                      / \
                 r   c   f          r---c   f
                  \   \ /                \
                   a---b              a---b

     Figure 5: The two maximally redundant trees found in the network
                       depicted in previous figure.

   Now, a simple example is in order.  Consider the network depicted in
   Figure 4, and suppose that the common root is node r.  We have only r
   in the trees, so we select one of its neighbors, let it be a, remove
   the link between them, and select a path (let it be the shortest one)
   from a to r; this path is a-b-c-r, so the ear is r-a-b-c-r.  Since
   both endpoints of the ear are r, selecting the right tree is not
   important, e.g., we can add c-b-a-r to the first tree, and a-b-c-r to
   the second one Figure 5.  This way, r, a, b and c form the set of
   "ready" nodes.  From the ready set, c and d are not the root and have
   non-ready neighbors.  Let us select, e.g., c.  The shortest path from
   d to r when c is removed is d-e-r, so we have ear c-d-e-r, we add
   d-e-r to the first tree and e-d-c to the second one (recall that we
   do not want to create a new neighbor for r in the second tree).
   Finally, the last non-ready node is f, and the ear is b-f-d.  Since
   neither is b an ancestor of d nor is d an ancestor of b in any of the
   trees, we can connect f to the trees in both ways.  E.g., add f-b to
   the first tree, and f-d to the second one.

A.2.  Non-2-connected networks

   When, however, the network is not 2-connected, it is not always
   possible to find a pair of node-disjoint paths from any node x to
   root r, which makes our previous algorithm unable to find the trees.
   However, while the network is connected, it is made up by 2-connected
   components bordered by "cut-vertices" (naturally, some of these
   components may contain only one node).  A node is a cut-vertex, if
   removing that node splits the network into two.

   A simple algorithm to find the components and the cut-vertices can be
   to (virtually) remove each vertex one by one, and check connectivity

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   with BFS or DFS.  Moreover, nodes a and b are in the same 2-connected
   component, if a remains reachable from b after removing any single
   node.  Note that linear time algorithms do exist that find both the
   2-connected components and the cut-vertices.

   Now, we can build up redundant trees in each component.  In
   components containing r, the root of such trees must be r.
   Otherwise, in the remaining components the root must be the last node
   in the component along a path to the root.  Recall, that this must be
   a cut-vertex, so it is the same for each path emanating from that

   At this point, we are ready, if there is no cut-edge in the network.
   However, if some 2-connected components are connected by a cut-edge,
   we must add that edge to both of the trees.

                       e---d      i
                      /   / \    /|
                     r---c   f--g |
                      \   \ /    \|
                       a---b      j

                     Figure 6: Non-2-connected network

              e---d      i         e---d      i
             /          /|            / \     |
            r   c   f--g |       r---c   f--g |
             \   \ /     |            \      \|
              a---b      j         a---b      j

     Figure 7: The two maximally redundant trees found in the network
                           depicted previously.

   As an example consider the network depicted in Figure 6.  Observe
   that now we have two 2-connected components, one contains r, a, b, c,
   d, e, f and the other contains g, i, j.  Moreover, these components
   have no common node, they are connected with a cut-edge.

   Finding the trees in the component containing r is already described;
   these trees are the same as previously.  Moreover, the other
   component is a cycle, so it will be covered by a single ear.  Finally
   we must add link f-g to both of the trees, to get the trees depicted
   in Figure 7.

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A.3.  Finding maximally redundant trees in distributed environment

   If we need to compute exactly the same maximally redundant trees at
   each of the routers, consistency needs to be ensured by tie-breaking
   mechanisms.  Observe that the previous algorithm has multiple choices
   when it selects how to connect nodes to the trees when only r is
   ready, how to select ready node q and non-ready node w for a later
   ear and when neither of the endpoints is an ancestor of the other

   All of the previous decision points can be handled in a consistent
   fashion.  E.g., the first ear should be connected in such a way, that
   the neighbor of r with the lowest ID must be directly connected to r
   in the first tree.  Moreover, later we should choose ready router
   with non-ready neighbor as q and its non-ready neighbor with the
   lowest ID as w.  Finally, when neither of the endpoint is an ancestor
   of the other one, connect the ear to the endpoint with the lower ID
   in the first tree.

Authors' Addresses

   Alia Atlas (editor)
   Juniper Networks
   10 Technology Park Drive
   Westford, MA  01886


   Maciek Konstantynowicz
   Juniper Networks


   Gabor Sandor Enyedi
   Irinyi utca 4-10
   Budapest  1117


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   Andras Csaszar
   Irinyi J ut 4-10
   Budapest  1117


   Russ White
   Cisco Systems


   Mike Shand
   Cisco Systems


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