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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
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 56 (9 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
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 49 (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...
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 48 (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
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 45 (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
"... ..., 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 43 (11 self)
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..., 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.
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 35 (5 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
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 33 (1 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.
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,