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43
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 53 (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
Hardness of the undirected edgedisjoint paths problem
 Proc. of STOC
, 2005
"... In the EdgeDisjoint Paths problem with Congestion (EDPwC), we are given a graph with n nodes, a set of terminal pairs and an integer c. The objective is to route as many terminal pairs as possible, subject to the constraint that at most c demands can be routed through any edge in the graph. When c ..."
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Cited by 50 (8 self)
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In the EdgeDisjoint Paths problem with Congestion (EDPwC), we are given a graph with n nodes, a set of terminal pairs and an integer c. The objective is to route as many terminal pairs as possible, subject to the constraint that at most c demands can be routed through any edge in the graph. When c = 1, the problem is simply referred to as the EdgeDisjoint Paths (EDP) problem. In this paper, we study the hardness of EDPwC in undirected graphs. We obtain an improved hardness result for EDP, and also show the first polylogarithmic integrality gaps and hardness of approximation results for EDPwC. Specifically, we prove that EDP is (log 1 2 −ε n)hard to approximate for any constant ε> 0, unless NP ⊆ ZP T IME(n polylog n). We also show that for any congestion c = o(log log n / log log log n), there is no (log 1−ε c+1 n)approximation algorithm for EDPwC, unless NP ⊆ ZP T IME(npolylog n). For larger congestion, where c ≤ η log log n / log log log n for some constant η, we obtain superconstant inapproximability ratios. All of our hardness results can be converted into integrality gaps for the multicommodity flow relaxation. We also present a separate elementary direct proof of this integrality gap result. Finally, we note that similar results can be obtained for the AllorNothing Flow (ANF) problem, a relaxation of EDP, in which the flow unit routed between the sourcesink pairs does not have follow a single path, so the resulting flow is not necessarily integral. Using standard transformations, our results also extend to the nodedisjoint versions of these problems as well as to the directed setting. 1
Computing Nash equilibria for scheduling on restricted parallel links
 In Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC
, 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. Thus, the problem is equivalent to the correspondingly restricted problem of assigning n jobs to m parallel machines. In ..."
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Cited by 48 (8 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. Thus, the problem is equivalent to the correspondingly restricted problem of assigning n jobs to m parallel machines. In a pure Nash equilibrium, no user may improve its own individual cost (delay) by unilaterally switching to another link from its set of allowed links. As our main result, we introduce a polynomial time algorithm to compute from any given assignment a pure Nash equilibrium with nonincreased makespan. The algorithm gradually changes a given assignment by pushing unsplittable user traffics through a network that is defined by the users and the links. Here, we use ideas from blocking flows. Furthermore, we use similar techniques as in the generic PreflowPush algorithm to approximate a schedule with minimum makespan, gaining an improved approximation factor of 2 − 1 for identical links, where w1 is the largest user traffic. w1 We extend this result to related links, gaining an approximation factor of 2. Our approximation algorithms run in polynomial time. We close with tight upper bounds on the coordination ratio for pure Nash equilibria.
Approximating the SingleSink Link Installation Problem in Network Design
, 1998
"... We initiate the algorithmic study of an important but NPhard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem v , for each source node v. (2) ..."
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Cited by 44 (2 self)
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We initiate the algorithmic study of an important but NPhard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem v , for each source node v. (2) A small set of cable types, where each cable type is specified by its capacity and its cost per unit length. The cost per unit capacity per unit length of a highcapacity cable may be significantly less than that of a lowcapacity cable, reflecting an economy of scale, i.e., the payoff for buying at bulk may be very high. The goal is to design a minimumcost network that can (simultaneously) route all the demands at the sources to the sink, by installing zero or more copies of each cable type on each edge of the graph. An additional restriction is that the demand of each source must follow a single path. The problem is to find a route from each source node to the sink and to assign ca...
Improved approximation algorithms for unsplittable flow problems (Extended Abstract)
 In Proceedings of the 38th Annual Symposium on Foundations of Computer Science
, 1997
"... ) Stavros G. Kolliopoulos 1 Clifford Stein 1 Abstract In the singlesource unsplittable flow problem we are given a graph G; a source vertex s and a set of sinks t 1 ; : : : ; t k with associated demands. We seek a single st i flow path for each commodity i so that the demands are satisfied and ..."
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Cited by 42 (2 self)
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) Stavros G. Kolliopoulos 1 Clifford Stein 1 Abstract In the singlesource unsplittable flow problem we are given a graph G; a source vertex s and a set of sinks t 1 ; : : : ; t k with associated demands. We seek a single st i flow path for each commodity i so that the demands are satisfied and the total flow routed across any edge e is bounded by its capacity c e : The problem is an NPhard variant of max flow and a generalization of singlesource edgedisjoint paths with applications to scheduling, load balancing and virtualcircuit routing problems. In a significant development, Kleinberg gave recently constantfactor approximation algorithms for several natural optimization versions of the problem [18]. In this paper we give a generic framework that yields simpler algorithms and significant improvements upon the constant factors. Our framework, with appropriate subroutines, applies to all optimization versions previously considered and treats in a unified manner directed and u...
The AllorNothing Multicommodity Flow Problem
 in Proceedings of the 36th ACM Symposium on Theory of Computing (STOC
, 2004
"... m)), the same as that for edp [10]. Our algorithm extends to the case where each pair siti has a demand di associated with it and we need to completely route di to get credit for pair i. We also consider the online admission control version where pairs arrive online and the algorithm has to decide i ..."
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Cited by 40 (10 self)
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m)), the same as that for edp [10]. Our algorithm extends to the case where each pair siti has a demand di associated with it and we need to completely route di to get credit for pair i. We also consider the online admission control version where pairs arrive online and the algorithm has to decide immediately on its arrival whether to accept it or not. We obtain a randomized algorithm with a competitive ratio that is similar to the approximation ratio for the offline algorithm. \Lambda
On the SingleSource Unsplittable Flow Problem
, 1998
"... Let G = (V; E) be a capacitated directed graph with a source s and k terminals t i with demands d i , 1 i k. We would like to concurrently route every demand on a single path from s to the corresponding terminal without violating the capacities. There are several interesting and important varia ..."
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Cited by 39 (2 self)
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Let G = (V; E) be a capacitated directed graph with a source s and k terminals t i with demands d i , 1 i k. We would like to concurrently route every demand on a single path from s to the corresponding terminal without violating the capacities. There are several interesting and important variations of this unsplittable flow problem. If the
HopbyHop Routing Algorithms for PremiumClass Traffic in DiffServ Networks
, 2002
"... Bear the provision of Quality of Service (QoS) in the Internet, Differentiated Service (DiffServ) model has been proposed as a costeffective solution. Traffic is classified into several service classes with different priorities. The premium class traffic has the highest one. The routing algorithm ..."
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Cited by 30 (2 self)
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Bear the provision of Quality of Service (QoS) in the Internet, Differentiated Service (DiffServ) model has been proposed as a costeffective solution. Traffic is classified into several service classes with different priorities. The premium class traffic has the highest one. The routing algorithm used by the premium class service has significant effects not only on its own traffic, but on all other classes of traffic as well. The shortest hopcount routing scheme used in current Internet turns out to be no longer sufficient in DiffServ networks. Based on
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 23 (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
Multipath Routing Algorithms for Congestion Minimization
, 2007
"... Unlike traditional routing schemes that route all traffic along a single path, multipath routing strategies split the traffic among several paths in order to ease congestion. It has been widely recognized that multipath routing can be fundamentally more efficient than the traditional approach of ro ..."
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Cited by 18 (0 self)
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Unlike traditional routing schemes that route all traffic along a single path, multipath routing strategies split the traffic among several paths in order to ease congestion. It has been widely recognized that multipath routing can be fundamentally more efficient than the traditional approach of routing along single paths. Yet, in contrast to the singlepath routing approach, most studies in the context of multipath routing focused on heuristic methods. We demonstrate the significant advantage of optimal (or near optimal) solutions. Hence, we investigate multipath routing adopting a rigorous (theoretical) approach. We formalize problems that incorporate two major requirements of multipath routing. Then, we establish the intractability of these problems in terms of computational complexity. Finally, we establish efficient solutions with proven performance guarantees.