Initialization: Loop until all nodes in N
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1 Routing Routing lgorithm classification Routing protocol Goal: determine good path (sequence of routers) thru netork from source to dest. Graph abstraction for routing s: graph nodes are routers graph edges are physical links link cost: delay, $ cost, or congestion level good path: F typically means minimum cost path other def s possible Global or decentralized information? Global: all routers have complete topology, link cost info link state s ecentralized: router knos physicallyconnected neighbors, link costs to neighbors iterative process of computation, exchange of info ith neighbors distance vector s Static or dynamic? Static: routes change sloly over time ynamic: routes change more quickly periodic update in response to link cost changes : Netork Layer a-9 : Netork Layer a-0 Link-State Routing lgorithm ijkstra s net topology, link costs knon to all nodes accomplished via link state broadcast all nodes have same info computes least cost paths from one node ( source ) to all other nodes gives routing table for that node iterative: after k iterations, kno least cost path to k dest. s Notation: c(i,j): link cost from node i to j. cost infinite if not direct neighbors (v): current value of cost of path from source to dest. V p(v): predecessor node along path from source to v, that is next v N: set of nodes hose least cost path definitively knon : Netork Layer a- ijsktra s lgorithm Initialization: N = {} for all nodes v if v adjacent to then (v) = c(,v) ; p(v) = else (v) = Loop 9 find not in N such that () is a minimum 0 add to N update (v) for all v adjacent to and not in N: If ( (v) > () + c(,v) ) { (v) = () + c(,v)) p(v) = } /* ne cost to v is either old cost to v or knon shortest path cost to plus cost from to v */ until all nodes in N : Netork Layer a-
2 Step 0 ijkstra s : example start N F (),p(),,, (),p(),,,, (),p(), F (),p(), (F),p(F),,, : Netork Layer a- ijsktra s lgorithm Revisited Initialization: N = {} for all nodes v if v adjacent to then (v) = c(,v) ; n(v) = v else (v) = Loop 9 find not in N such that () is a minimum 0 add to N update (v) for all v adjacent to and not in N: If ( (v) > () + c(,v) ) { (v) = () + c(,v)) n(v) = n() } /* ne cost to v is either old cost to v or knon shortest path cost to plus cost from to v */ until all nodes in N : Netork Layer a- ijkstra s, discussion istance Vector Routing lgorithm lgorithm complexity: n nodes Naïve: each iteration: need to check all nodes,, not in N n*(n+)/ comparisons: O(n**) more efficient implementations possible: O(nlogn) (hat data structure?) : Netork Layer a- iterative: continues until no nodes exchange info. self-terminating: no signal to stop asynchronous: nodes need not exchange info/iterate in lock step! distributed: each node communicates only ith directly-attached neighbors istance Table data structure each node has its on ro for each possible column for each directlyattached neighbor to node example: in node, for dest. via neighbor : (,) = = distance from to, via as next hop c(,) + min { (,)} : Netork Layer a-
3 istance Table: example istance table gives routing table (,) (,) (,) = c(,) + min { (,)} = + = = c(,) + min { (,)} = + = loop! = c(,) + min { (,)} = + = () cost to via 9 () cost to via 9 istance table Outgoing link to use, cost,,,, Routing table : Netork Layer a- : Netork Layer a- istance Vector Routing: overvie istance Vector lgorithm: Iterative, asynchronous: each local iteration caused by: local link cost change message from neighbor: its least cost path change from neighbor istributed: each node notifies neighbors only hen its least cost path to any changes neighbors then notify their neighbors if necessary ach node: ait for (change in local link cost or msg from neighbor) recompute distance table if least cost path to any dest has changed, notify neighbors : Netork Layer a-9 t all nodes, : Initialization: for all adjacent nodes v: (*,v) = /* the * operator means "for all ros" */ (v,v) = c(,v) for all s, y send min (y,) to each neighbor /* over all 's neighbors */ : Netork Layer a-0
4 istance Vector lgorithm (cont.): loop 9 ait (until I see a link cost change to neighbor V 0 or until I receive update from neighbor V) if (c(,v) changes by d) /* change cost to all dest's via neighbor v by d */ /* note: d could be positive or negative */ for all s y: (y,v) = (y,v) + d else if (update received from V rt ) /* shortest path from V to some has changed */ 9 /* V has sent a ne value for its min V(,) */ 0 /* call this received ne value is "neval" */ for the single y: (,V) = c(,v) + neval if e have a ne min (,)for any send ne value of min (,) to all neighbors forever : Netork Layer a- istance Vector lgorithm: example : Netork Layer a- istance Vector lgorithm: example istance Vector: link cost changes (,) = c(,) + min { (,)} = + = (,) = c(,) + min { (,)} = + = Link cost changes: node detects local link cost change updates distance table (line ) if cost change in least cost path, notify neighbors (lines,) good nes travels fast 0 terminates : Netork Layer a- : Netork Layer a-
5 istance Vector: link cost changes istance Vector: poisoned reverse Link cost changes: good nes travels fast bad nes travels slo - count to problem! 0 0 If routes through to get to : tells its ( s) distance to is infinite (so on t route to via ) ill this completely solve count to problem? 0 0 continues on! terminates : Netork Layer a- : Netork Layer a- omparison of LS and V s Message complexity LS: ith n nodes, links, O(n) msgs sent each V: exchange beteen neighbors only convergence time varies Speed of onvergence LS: O(n**) requires O(n) msgs may have oscillations V: convergence time varies may be routing loops count-to- problem Robustness: hat happens if router malfunctions? LS: node can advertise incorrect link cost each node computes only its on table V: V node can advertise incorrect path cost each node s table used by others error propagate thru netork : Netork Layer a-
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