An online throughput-competitive algorithm for multicast routing and admission control

We present the first polylog-competitive online algorithm for the general multicast admission control and routing problem in the throughput model. The ratio of the number of requests accepted by the optimum offline algorithm to the expected number of requests accepted by our algorithm is O((logn+loglogM) (logn+logM)logn), where M is the number of multicast groups and n is the number of nodes in the graph. We show that this is close to optimum by presenting an 0(lognlogM) lower bound on this ratio for any randomized online algorithm against an oblivious adversary, when M is much larger than the link capacities. Our lower bound applies even in the restricted case where the link capacities are much larger than bandwidth requested by a single multicast. We also present a simple proof showing that it is impossible to be competitive against an adaptive online adversary. As in the previous online routing algorithms, our algorithm uses edge-costs when deciding on which is the best path to use. In contrast to the previous competitive algorithms in the throughput model, our cost is not a direct function of the edge load. The new cost definition allows us to decouple the effects of routing and admission decisions of different multicast groups.

Online throughput-competitive algorithm for multicast routing and admission control

Ashish Goel, Monika Henzinger

We present the first polylog-competitive online algorithm for the general multicast problem in the throughput model. The ratio of the number of requests accepted by the optimum offline algorithm to the expected number of requests accepted by our algorithm is O((log n+log log M)(log n+log M)log n), where M is the number of multicast groups and n is the number of nodes in the graph. We show that this is close to optimum by presenting an O(log n log M) lower bound on this ratio for any randomized online algorithm against an oblivious adversary, when M is much larger than the link capacities. Our lower bound applies even in the restricted cause where the link capacities are much larger than bandwidth requested by a single multicast. We also present a simple proof showing that it is impossible to be competitive against an adaptive online adversary. As in the previous online routing algorithms, our algorithm uses edge-costs when deciding on which is the best path to use. In contrast to the previous competitive algorithms in the throughput model, our cost is not a direct function of the edge load. The new cost definition allows us to decouple the effects of routing and admission decisions of different multicast groups.

SIAM1998

Problèmes de cheminements optimaux dans les réseaux avec contraintes associées aux arcs

In this thesis we consider two optimal routing problems in networks. Both are NP-hard and are often used to modelize real life problems of large size. We first present the capacitated arc routing problem (CARP). In this problem, we have to serve a set of customers represented by the arcs of a network with vehicles of restricted capacity. The aim is to design a set of vehicle routes of least total cost. We describe two heuristic methods for the CARP based on local search techniques. The first one is a Tabu Search heuristic using an original post-optimization procedure. Principles appearing in this procedure are used to define a class of neighborhoods we combine in a Variable Neighborhood Descent method. Our algorithms compare favorably with some of her methods. They were initially developed to deal with the undirected CARP. We describe how to transform them so that they can be applied to the directed CARP. We also propose an adaptation to the directed case of a lower bound originally developed for the undirected CARP. This lower bound is used to evaluate the quality of the solutions produced by our algorithms for the directed CARP. Our methods obtain solutions whose value is, on average, close to known lower bounds. We use the CARP to tackle a real life problem of boat routing and scheduling. This problem can be viewed as a directed CARP with time windows. We describe in detail its modeling process and we analyze our first results. We obtain solutions that require less boats than the present schedule. Nevertheless, these solutions are not completely feasible in practice. We suggest some ways to improve them. The second problem treated in this thesis is the shortest capacitated paths problem (SCPP). We present a Tabu Search heuristic and some post-optimization procedures for the SCPP. These procedures are called in our Tabu Search algorithm. Two versions of this algorithm are considered. In the first one, post-optimization procedures are intensively used. In the second one, they are less frequently applied. This second version is faster. Compared with a greedy approach, the two versions of our Tabu Search heuristic obtain solutions which are, on average, of better quality. The SCPP was proposed to us by EDF (Electricité de France) in order to minimize the total length of the paths followed by cables in a nuclear power-station. It can also be viewed as a subproblem of the bandwidth packing problem (BWP) appearing in telecommunications.

EPFL2000

Scheduling multicasts on unit-capacity trees and meshes

Monika Henzinger

This paper studies the multicast routing and admission control problem on unit-capacity tree and mesh topologies in the throughput-model. The problem is a generalization of the edge-disjoint paths problem and is NP-hard both on trees and meshes. We study both the online and the online version of the problem: In the offline setting, we give the first constant-factor approximation algorithm for trees, and an O((log log n)2)-factor approximation algorithm for meshes, where n is the number of nodes in the graph. In the online setting, we give the first polylogarithmic competitive online algorithm for tree and mesh topologies. No polylogarithmic-competitive algorithm is possible on general network topologies and there exists a polylogarithmic lower bound on the competitive ratio of any online algorithm on tree topologies. We prove the same lower bound for meshess.

SIAM1999

Problèmes de cheminements optimaux dans les réseaux avec contraintes associées aux arcs

EPFL2000