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33
Graph problems arising from wavelengthrouting in alloptical networks
, 1997
"... We survey the theoretical results obtained for wavelength routing in all–optical networks, present some new results and propose several open problems. In all–optical networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry s ..."
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Cited by 82 (23 self)
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We survey the theoretical results obtained for wavelength routing in all–optical networks, present some new results and propose several open problems. In all–optical networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. The information, once transmitted as light, reaches its destination without being converted to electronic form in between, thus reaching high data transmission rates. We consider both networks with arbitrary topologies and particular networks of practical interest.
Approximating the Throughput of Multiple Machines in RealTime Scheduling
"... We consider the following fundamental scheduling problem. The input to the problem consists of n jobs and k machines. Each of the jobs is associated with a release time, a deadline, a weight, and a processing time on each of the machines. The goal is to find a schedule that maximizes the weight of j ..."
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Cited by 57 (6 self)
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We consider the following fundamental scheduling problem. The input to the problem consists of n jobs and k machines. Each of the jobs is associated with a release time, a deadline, a weight, and a processing time on each of the machines. The goal is to find a schedule that maximizes the weight of jobs that meet their deadline. We give constant factor approximation algorithms for four variants of the problem, depending on the type of the machines (identical vs. unrelated), and the weight of the jobs (identical vs. arbitrary). All these variants are known to be NPHard, and we observe that the two variants involving unrelated machines are also MAXSNP hard. To the best of our knowledge, these are the first approximation algorithms for such problems in the nonpreemptive o line setting. The specific results obtained are:  For identical job weights and unrelated machines: a greedy 2approximation algorithm.  For identical job weights and k identical machines: the same greedy alg...
Lower Bounds for Online Graph Problems with Application to Online Circuit and Optical Routing
, 1996
"... We present lower bounds on the competitive ratio of randomized algorithms for a wide class of online graph optimization problems and we apply such results to online virtual circuit and optical routing problems. Lund and Yannakakis [LY93a] give inapproximability results for the problem of finding t ..."
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Cited by 54 (11 self)
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We present lower bounds on the competitive ratio of randomized algorithms for a wide class of online graph optimization problems and we apply such results to online virtual circuit and optical routing problems. Lund and Yannakakis [LY93a] give inapproximability results for the problem of finding the largest vertex induced subgraph satisfying any nontrivial, hereditary, property . E.g., independent set, planar, acyclic, bipartite, etc. We consider the online version of this family of problems, where some graph G is fixed and some subgraph H is presented online, vertex by vertex. The online algorithm must choose a subset of the vertices of H , choosing or rejecting a vertex when it is presented, whose vertex induced subgraph satisfies property . Furthermore, we study the online version of graph coloring whose offline version has also been shown to be inapproximable [LY93b], online max edgedisjoint paths and online path coloring problems. Irrespective of the time complexity, w...
OnLine Randomized Call Control Revisited
 SIAM J. COMPUTING
, 2001
"... We consider the problem of online call admission and routing on trees and meshes. Previous work gave randomized online algorithms for these problems and proved that they have optimal (up to constant factors) competitive ratios. However, these algorithms can obtain very low profit with high probabi ..."
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Cited by 32 (8 self)
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We consider the problem of online call admission and routing on trees and meshes. Previous work gave randomized online algorithms for these problems and proved that they have optimal (up to constant factors) competitive ratios. However, these algorithms can obtain very low profit with high probability. We investigate the question of devising for these problems online competitive algorithms that also guarantee a "good" solution with "good" probability. We give a new
OnLine Routing in AllOptical Networks
 IN PROCEEDINGS OF THE 24TH INTERNATIONAL COLLOQIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING, LNCS 1256
, 1997
"... The paper deals with online routing in WDM (wavelength division multiplexing) optical networks. A sequence of requests arrives over time, each is a pair of nodes to be connected by a path. The problem is to assign a wavelength and a path to each pair, so that no two paths sharing a link are assigne ..."
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Cited by 31 (7 self)
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The paper deals with online routing in WDM (wavelength division multiplexing) optical networks. A sequence of requests arrives over time, each is a pair of nodes to be connected by a path. The problem is to assign a wavelength and a path to each pair, so that no two paths sharing a link are assigned the same wavelength. The goal is to minimize the number of wavelengths used to establish all connections. Raghavan and Upfal [RU94] considered the offline version of the problem, which was further studied in [AR95, KP96, MKR95, Ra96]. For a line topology, the problem is the wellstudied interval graph coloring problem. Online algorithms for this problem have been analyzed in [KT81, Ki88]. We consider trees, trees of rings, and meshes topologies, previously studied in the offline case. We give online algorithms with competitive ratio O(log n) for all these topologies. We give a matching \Omega\Gammaing n) lower bound for meshes. We also prove that any algorithm for trees canno...
Beating the Logarithmic Lower Bound: Randomized Preemptive Disjoint Paths and Call Control Algorithms
 in Proc. 10th ACMSIAM Symp. on Discrete Algorithms
, 1998
"... We consider the maximum disjoint paths problem and its generalization, the call control problem, in the online setting. In the maximum disjoint paths problem, we are given a sequence of connection requests for some communication network. Each request consists of a pair of nodes, that wish to com ..."
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Cited by 22 (4 self)
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We consider the maximum disjoint paths problem and its generalization, the call control problem, in the online setting. In the maximum disjoint paths problem, we are given a sequence of connection requests for some communication network. Each request consists of a pair of nodes, that wish to communicate over a path in the network. The request has to be immediately connected or rejected, and the goal is to maximize the number of connected pairs, such that no two paths share an edge. In the call control problem, each request has an additional bandwidth speci cation, and the goal is to maximize the total bandwidth of the connected pairs (throughput), while satisfying the bandwidth constraints (assuming each edge has unit capacity). These classical problems are central in routing and admission control in high speed networks and in optical networks.
The Maximum EdgeDisjoint Paths Problem In Bidirected Trees
 SIAM Journal on Discrete Mathematics
, 1998
"... . A bidirected tree is the directed graph obtained from an undirected tree by replacing each undirected edge by two directed edges with opposite directions. Given a set of directed paths in a bidirected tree, the goal of the maximum edgedisjoint paths problem is to select a maximumcardinality subse ..."
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Cited by 17 (3 self)
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. A bidirected tree is the directed graph obtained from an undirected tree by replacing each undirected edge by two directed edges with opposite directions. Given a set of directed paths in a bidirected tree, the goal of the maximum edgedisjoint paths problem is to select a maximumcardinality subset of the paths such that the selected paths are edgedisjoint. This problem can be solved optimally in polynomial time for bidirected trees of constant degree, but is MAXSNPhard for bidirected trees of arbitrary degree. For every fixed " ? 0, a polynomialtime (5=3+ ")approximation algorithm is presented. Key words. approximation algorithms, edgedisjoint paths, bidirected trees AMS subject classifications. 68Q25, 68R10 1. Introduction. Research on disjoint paths problems in graphs has a long history [12]. In recent years, edgedisjoint paths problems have been brought into the focus of attention by advances in the field of communication networks. Many modern network architectures estab...
Maximizing the Number of Connections in Optical Tree Networks
 In Proceedings of the 9th Annual International Symposium on Algorithms and Computation (1998), LNCS 1533
, 1998
"... . In optical networks with wavelength division multiplexing (WDM), multiple connections can share a link if they are transmitted on different wavelengths. We study the problem of satisfying a maximum number of connection requests in a directed tree network if only a limited number W of wavelength ..."
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Cited by 15 (4 self)
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. In optical networks with wavelength division multiplexing (WDM), multiple connections can share a link if they are transmitted on different wavelengths. We study the problem of satisfying a maximum number of connection requests in a directed tree network if only a limited number W of wavelengths are available. In optical networks without wavelength converters this is the maximum path coloring (MaxPC) problem, in networks with full wavelength conversion this is the maximum path packing (MaxPP) problem. MaxPC and MaxPP are shown to be polynomialtime solvable to optimality if the tree has height one or if both W and the degree of the tree are bounded by a constant. If either W or the degree of the tree is not bounded by a constant, MaxPC and MaxPP are proved NPhard. Polynomialtime approximation algorithms with performance ratio 5=3 + " for arbitrarily small " are presented for the case W = 1, in which MaxPC and MaxPP are equivalent. For arbitrary W , a 2approximation for MaxPP in arbitrary trees, a 1:58approximation for MaxPC in trees of bounded degree, and a 2:22approximation for MaxPC in arbitrary trees are obtained. 1
The Accommodating Function  a generalization of the competitive ratio
 In Sixth International Workshop on Algorithms and Data Structures, volume 1663 of Lecture Notes in Computer Science
, 1998
"... A new measure, the accommodating function, for the quality of online algorithms is presented. The accommodating function, which is a generalization of both the competitive ratio and the accommodating ratio, measures the quality of an online algorithm as a function of the resources that would be su ..."
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Cited by 14 (9 self)
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A new measure, the accommodating function, for the quality of online algorithms is presented. The accommodating function, which is a generalization of both the competitive ratio and the accommodating ratio, measures the quality of an online algorithm as a function of the resources that would be sufficient for an optimal algorithm to fully grant all requests. More precisely, if we have some amount of resources n, the function value at ff is the usual ratio (still on some fixed amount of resources n), except that input sequences are restricted to those where all requests could have been fully granted by an optimal algorithm if it had had the amount of resources ffn. The accommodating functions for three specific online problems are investigated: a variant of binpacking in which the goal is to maximize the number of objects put in n bins, the seat reservation problem, and the problem of optimizing total flow time when preemption is allowed.
Competitive Call Control in Mobile Networks
 In Proceedings of International Symposium on Algorithms and Computation (ISAAC '97), LNCS 1350
, 1997
"... In this paper, we deal with competitive local online algorithms for nonpreemptive channel allocation in mobile networks. The signal interferences in a network are modeled using an interference graph G. We prove that the greedy online algorithm is \Deltacompetitive, where \Delta is the maximum de ..."
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Cited by 13 (3 self)
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In this paper, we deal with competitive local online algorithms for nonpreemptive channel allocation in mobile networks. The signal interferences in a network are modeled using an interference graph G. We prove that the greedy online algorithm is \Deltacompetitive, where \Delta is the maximum degree of G. We employ the "classify and randomly select" paradigm ([5, 13]), and give a 5competitive randomized algorithm for the case of planar interference graphs, and 2competitive randomized algorithm for the case that the interference graph is a tree. We also show that the problem of call control in mobile networks with multiple available frequencies reduces to the problem of call control in mobile networks with a single frequency. Using this reduction, we present online algorithms for general networks with a single frequency. We give a local online algorithm which is ff(ffi+1+ff) (1=2+ff) 2 competitive, where ff is the independence number of G, and ffi is the average degree of G ....