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47
Fairness in routing and load balancing
 J. Comput. Syst. Sci
, 1999
"... We consider the issue of network routing subject to explicit fairness conditions. The optimization of fairness criteria interacts in a complex fashion with the optimization of network utilization and throughput; in this work, we undertake an investigation of this relationship through the framework o ..."
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Cited by 74 (0 self)
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We consider the issue of network routing subject to explicit fairness conditions. The optimization of fairness criteria interacts in a complex fashion with the optimization of network utilization and throughput; in this work, we undertake an investigation of this relationship through the framework of approximation algorithms. In a range of settings including both highspeed networks and Internet applications, maxmin fairness has emerged as a widely accepted formulation of the notion of fairness. Informally, we say that an allocation of bandwidth is maxmin fair if there is no way to give more bandwidth to any connection without decreasing the allocation to a connection of lesser or equal bandwidth. Given a collection of transmission routes, this criterion imposes a certain equilibrium condition on the bandwidth allocation, and some simple flow control mechanisms converge quickly to this equilibrium state. Indeed, the vast majority of previous work on maxmin fairness has focused on this issue of associating rates with connections that are specified by a fixed set of paths. Very little work has been devoted to understanding the relationship between the way in which one selects paths
Computing nash equilibria for scheduling on restricted parallel links
 In Proceedings of the 36th Annual ACM Symposium on the Thoery of Computing (STOC’04
, 2004
"... We consider the problem of routing n users on m parallel links under the restriction that each user may only be routed on a link from a certain set of allowed links for the user. So, this problem is equivalent to the correspondingly restricted scheduling problem of assigning n jobs to m parallel ma ..."
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Cited by 61 (12 self)
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We consider the problem of routing n users on m parallel links under the restriction that each user may only be routed on a link from a certain set of allowed links for the user. So, this problem is equivalent to the correspondingly restricted scheduling problem of assigning n jobs to m parallel machines. In a Nash equilibrium, no user may improve its own Individual Cost (latency) by unilaterally switching to another link from its set of allowed links. For identical links, we present, as our main result, a polynomial time algorithm to compute from any given assignment a Nash equilibrium with nonincreased makespan. The algorithm gradually transforms the assignment by pushing the unsplittable user traffics through a flow network, which is constructed from the users and the links. The algorithm uses ideas from blocking flows. Furthermore, we use techniques simular to those in the generic PREFLOWPUSH algorithm to approximate in polynomial time a schedule with optimum makespan. This results to an improved approximation factor of 2 − 1w1 for identical links, where w1 is the largest user traffic, and to an approximation factor of 2 for related links. 2
On the kSplittable Flow Problem
, 2002
"... In traditional multicommodity flow theory, the task is to send a certain amount of each commodity from its start to its target node, subject to capacity constraints on the edges. However, ..."
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Cited by 29 (3 self)
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In traditional multicommodity flow theory, the task is to send a certain amount of each commodity from its start to its target node, subject to capacity constraints on the edges. However,
Approximation algorithms for singlesource unsplittable flow
 SIAM Journal on Computing
, 2002
"... In the singlesource unsplittable flow problem, commodities must be routed simultaneously from a common source vertex to certain sinks in a given graph with edge capacities. The demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacit ..."
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Cited by 26 (4 self)
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In the singlesource unsplittable flow problem, commodities must be routed simultaneously from a common source vertex to certain sinks in a given graph with edge capacities. The demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. This problem was introduced by Kleinberg [1996a] and generalizes several NPcomplete problems. A cost value per unit of flow may also be defined for every edge. In this paper, we implement the 2approximation algorithm of Dinitz, Garg, and Goemans [1999] for congestion, which is the best known, and the (3, 1)approximation algorithm of Skutella [2002] for congestion and cost, which is the best known bicriteria approximation. We study experimentally the quality of approximation achieved by the algorithms and the effect of heuristics on their performance. We also compare these algorithms against the previous best ones by Kolliopoulos and Stein [1999] Categories and Subject Descriptors: G.2.2 [Discrete Mathematics]: Graph Algorithms—Graph
Parameterized tractability of edgedisjoint paths on directed acyclic graphs
 Proceedings of the 11th Annual European Symposium on Algorithms, ESA ’03, volume 2832 of Lecture Notes in Computer Science
, 2003
"... Given a graph and terminal pairs (si, ti), i ∈ [k], the edgedisjoint paths problem is to determine whether there exist siti paths, i ∈ [k], that do not share any edges. We consider this problem on acyclic digraphs. It is known to be NPcomplete and solvable in time n O(k) where n is the number of n ..."
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Cited by 22 (1 self)
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Given a graph and terminal pairs (si, ti), i ∈ [k], the edgedisjoint paths problem is to determine whether there exist siti paths, i ∈ [k], that do not share any edges. We consider this problem on acyclic digraphs. It is known to be NPcomplete and solvable in time n O(k) where n is the number of nodes. It has been a longstanding open question whether it is fixedparameter tractable in k, i.e. whether it admits an algorithm with running time of the form f(k) n O(1). We resolve this question in the negative: we show that the problem is W [1]hard, hence unlikely to be fixedparameter tractable. In fact it remains W [1]hard even if the demand graph consists of two sets of parallel edges. On a positive side, we give an O(m+k O(1) k! n) algorithm for the special case when G is acyclic and G + H is Eulerian, where H is the demand graph. We generalize this result (1) to the case when G + H is “nearly ” Eulerian, (2) to an analogous special case of the unsplittable flow problem, a generalized version of disjoint paths that has capacities and demands. Keywords. Disjoint paths, fixedparameter tractability, W[1]hardness, Eulerian graphs, unsplittable flow.
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines.Theor
 Comput. Sci
"... Abstract. We consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption. Job i takes processing time pij on machine j, and the total time used by a machine is the sum of the processing times for the jobs assigned to it. The objective is to minimize ma ..."
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Cited by 14 (2 self)
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Abstract. We consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption. Job i takes processing time pij on machine j, and the total time used by a machine is the sum of the processing times for the jobs assigned to it. The objective is to minimize makespan. The best known approximation algorithms for this problem compute an optimum fractional solution and then use rounding techniques to get an integral 2approximation. In this paper we present a combinatorial approximation algorithm that matches this approximation quality. It is much simpler than the previously known algorithms and its running time is better. This is the first time that a combinatorial algorithm always beats the interior point approach for this problem. Our algorithm is a generic minimum cost flow algorithm, without any complex enhancements, tailored to handle unsplittable flow. It pushes unsplittable jobs through a twolayered bipartite generalized network defined by the scheduling problem. In our analysis, we take advantage from addressing the approximation problem directly. In particular, we replace the classical technique of solving the LPrelaxation and rounding afterwards by a completely integral approach. We feel that this approach will be helpful also for other applications. 1
How good can IP routing be?
, 2001
"... In the traditional IP scheme, both the packet forwarding and the routing protocols are source invariant, i.e., their decisions depend on the destination IP address and not on the source address. Recent protocols, such as MPLS, as well as traditional circuit based protocols like PNNI allow routing de ..."
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Cited by 11 (0 self)
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In the traditional IP scheme, both the packet forwarding and the routing protocols are source invariant, i.e., their decisions depend on the destination IP address and not on the source address. Recent protocols, such as MPLS, as well as traditional circuit based protocols like PNNI allow routing decisions to depend on both the source and destination addresses. In fact, much of the theoretical work on routing assumes perflow forwarding and routing, i.e., the forwarding decision is based on both the source and destination addresses.
Minimizing Average Flowtime: Upper and Lower Bounds
, 2007
"... We consider the problem of minimizing average flow time on multiple machines when each job can be assigned only to a specified subset of the machines. This is a special case of scheduling on unrelated machines and we show that no online algorithm can have a bounded competitive ratio. We provide an O ..."
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Cited by 11 (4 self)
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We consider the problem of minimizing average flow time on multiple machines when each job can be assigned only to a specified subset of the machines. This is a special case of scheduling on unrelated machines and we show that no online algorithm can have a bounded competitive ratio. We provide an O(log P)approximation algorithm by modifying the singlesource unsplittable flow algorithm of Dinitz et.al. Here P is the ratio of the maximum to the minimum processing times. We establish an Ω(log P)integrality gap for our LPrelaxation and use this to show an Ω(log P / log log P) lower bound on the approximability of the problem. We then extend the hardness results to the problem of minimizing flow time on parallel machines and establish the first nontrivial lower bounds on the approximability; we show that the problem cannot be approximated to within Ω ( � log P / log log P).
On the Computational Complexity and Effectiveness of Nhub ShortestPath Routing
"... In this paper we study the computational complexity and effectiveness of a concept we term “Nhub ShortestPath Routing ” in IP networks. Nhub ShortestPath Routing allows the ingress node of a routing domain to determine up to N intermediate nodes (“hubs”) through which a packet will pass before r ..."
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Cited by 11 (1 self)
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In this paper we study the computational complexity and effectiveness of a concept we term “Nhub ShortestPath Routing ” in IP networks. Nhub ShortestPath Routing allows the ingress node of a routing domain to determine up to N intermediate nodes (“hubs”) through which a packet will pass before reaching its final destination. This facilitates better utilization of the network resources, while allowing the network routers to continue to employ the simple and wellknown shortestpath routing paradigm. Although this concept has been proposed in the past, this paper is the first to investigate it in depth. We apply Nhub ShortestPath Routing to the problem of minimizing the maximum load in the network. We show that the resulting routing problem is NPcomplete and hard to approximate. However, we propose efficient algorithms for solving it both in the online and the offline contexts. Our results show that Nhub ShortestPath Routing can increase network utilization significantly even for. Hence, this routing paradigm should be considered as a powerful mechanism for future datagram routing in the Internet.
The Demand Matching Problem
 In Proceedings of the 9th International Conference on Integer Programming and Combinatorial Optimization (IPCO
, 2002
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