Communication Systems Group (CSG) Policy-Compliant Path Diversity and Bisection Bandwidth Rowan Klöti 1, Vasileios Kotronis 1, Bernhard Ager 1, Xenofontas Dimitropoulos 2,1 1IEEE INFOCOM, April 2015, Hong Kong 1 ETH Zurich, Switzerland 2 University of Crete / FORTH, Greece Tuesday, 28 April 2015

Communication Systems Group (CSG) Assume that you are a network domain admin  How resilient is my AS-level connection to a remote AS?  What limits the path diversity between me and the remote AS?  My multi-homing degree?  The Internet topology at large?  Poor connectivity on the local/remote upstream ISPs’ side? 2IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015 *Picture from: / Me The other guy

Communication Systems Group (CSG) Consider an example network topology 3IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) We can perform a min-cut between S and D 4IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) We can calculate the maximum S-D flow 5IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) We can calculate the edge-disjoint S-D paths 6IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) Basic mechanism: min-cuts  Generalized problem: max-flow / min-cut  Basic theorem was proven back in 1956  Menger’s theorem  path diversity = min-cut, for unitary edge capacities  Well-known algorithms available  Well, then everything is already solved, right? 7IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) Networks are governed by policies  Motivation  Security considerations  Routing optimization techniques  Financial agreements, SLAs, …  Example 1: the “valley-free” AS-level Internet  Peers, providers, customers: p2p, p2c, c2p links  Example 2: (negative) waypoint routing  Force traffic into waypoints  Avoid certain nodes/links along the way 8IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015 c2p p2c p2p c2p p2c Peak

Communication Systems Group (CSG) Challenge: policies restrict path selection 9IEEE INFOCOM, April 2015, Hong Kong  Assume trivial regex policy: ( )* ( )+ ( )* Tuesday, 28 April 2015

Communication Systems Group (CSG) Challenge: policies restrict path selection 10IEEE INFOCOM, April 2015, Hong Kong  Only two edge-disjoint paths are now valid (min-cut=2) Tuesday, 28 April 2015

Communication Systems Group (CSG) Our contribution: estimating policy-compliant min-cuts  General methodology  Assumption: network policies as regular expressions  Graph transformation algorithm  Transformed graph contains only policy-compliant paths  Min-cut values should not be distorted by the transform  Min-cut calculations  Complex on original graph (no straightforward method)  Simple on transformed graph  No modification required on classic graph algorithms 11IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) How we represent graphs and policies  Network graph:  Network policy:  Valley-free example:  Graph = AS-level Internet  Policy = c2p*p2p?p2c* 12IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) Core of transformation: tensor product 13IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015  Intuition: move between G nodes and NFA states concurrently  Should yield valid, policy-compliant paths

Communication Systems Group (CSG) Does this process preserve the min-cut? 14IEEE INFOCOM, April 2015, Hong Kong                        Intuition: the min-cut paths between any 2 node sets in G’ should traverse at most the same number of || edges as in G Tuesday, 28 April 2015

Communication Systems Group (CSG) Idea: properly add aggregation states 15IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) Are all cases fully aggregatable? Aggregatable NFA cases  One-to-One  One-to-Many  Many-to-One  Many-to-Many Non-aggregatable NFA cases 16IEEE INFOCOM, April 2015, Hong Kong  Min-cut is inflated by a factor of 2  “Maximal biclique finding” problem Tuesday, 28 April 2015 Not a complete bipartite graph!

Communication Systems Group (CSG) Remember our initial motivation  How resilient is my AS-level connection to a remote AS?  What limits the path diversity between me and the remote AS?  My multi-homing degree?  The Internet topology at large?  Poor connectivity on the local/remote upstream ISPs’ side? 17IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015 *Picture from: / Me The other guy + POLICIES!

Communication Systems Group (CSG) Example I: Policies and AS-level path diversity  Classic Valley-Free (VF) vs Multi-Peering Links (MPL)  Graph based on CAIDA’s AS relationship dataset (+/- open p2p links from PeeringDB) 18IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015 c2p p2c p2p c2p p2c c2p p2c p2p c2p p2c p2p Plateau Peak

Communication Systems Group (CSG) Example II: Effect of depeering events  Simulated depeering between two tier-ones  Examined the effect on their exclusive customer cones  Valley-free  significant loss of path diversity  Multi-p2p links  negligible loss  Policy relaxation seems to be beneficial 19IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015 Inter-domain policy scenario Loss in mean path diversity after depeering(%) Valley-free Open Links7.02 Multiple Peering Links Open Links0.04

Communication Systems Group (CSG) Summary and Contributions  Estimating policy-compliant min-cuts on network graphs  Network policies as regular expressions  Graph transformation algorithm  Exact values or approximations depending on NFA form  Min-cut calculations  Complex on original graph  Simple on transformed graph  No modification required on classic graph algorithms  Large variety of use cases out there  AS-level path diversity under diverse policy models  MPTCP, multipath routing, flow routing applications 20IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) Questions? 21IEEE INFOCOM, April 2015, Hong Kong AS-level Internet POLICY- COMPLIANT MIN-CUTS Tuesday, 28 April 2015

Communication Systems Group (CSG) BACKUP 22IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) Assume that you are a datacenter operator  How resilient is my switched topology to link failures?  What is the bisection bandwidth of my datacenter? 23IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015 Picture from: /

Communication Systems Group (CSG) Min-cuts are the answer to many more questions  What is the max feasible bandwidth for a MPTCP transfer between two of my server clusters?  What is the bisection bandwidth of my datacenter?  How resilient is my switched topology to link failures?  How much edge capacity should be depleted for a successful DDoS link-flooding attack against my network?  What limits the AS-level path diversity between my domain and another remote domain?  My multi-homing degree?  The Internet topology at large?  Poor connectivity on the local/remote upstream providers’ side? 24IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) Complexity of the graph transform process  In space:  |V’| = O (|V|(|Q| + |Δ|)  |E’| = O (|Δ|(|V| + |E|)  In time:  t = O (|V||Q| + |Δ|(|V| + |E| + |Q|)) + t dec  In practice, the total running time is dominated by the min- cut calculation on the transformed graph 25IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) Related Work  Tensor products  Soule et al. use tensor products in a different context (bandwidth allocation policies)  Network resilience  Research on resilient networks  Network are not simply geographical maps  Policy-compliance framework is very important  Min-cuts with policies  Connectivity discovered by RV protocols by Sobrinho et al., valley-free s-t paths/cuts  Our main contribution: graph transformation without changing classic algorithms (can also be extended for finding the shortest valid paths), generic method 26IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) Inter-domain Routing Policy NFAs 27IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015

Communication Systems Group (CSG) NFA vs DFA (With Steps MPL scenario) 28IEEE INFOCOM, April 2015, Hong KongTuesday, 28 April 2015