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26
A still better performance guarantee for approximate graph coloring
, 1990
"... We present an approximation algorithm for graph coloring which achieves a performance guarantee of O(n(log log n) 2 =(log n) 3), a factor of log log n improvement. ..."
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Cited by 81 (7 self)
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We present an approximation algorithm for graph coloring which achieves a performance guarantee of O(n(log log n) 2 =(log n) 3), a factor of log log n improvement.
Making Commitments in the Face of Uncertainty: How to Pick a Winner Almost Every Time (Extended Abstract)
, 1996
"... In this paper, we formulate and provide optimal solutions for a broad class of problems in which a decisionmaker is required to select from among numerous competing options. The goal of the decisionmaker is to select the option that will have the best future performance. This task is made difficul ..."
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Cited by 55 (7 self)
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In this paper, we formulate and provide optimal solutions for a broad class of problems in which a decisionmaker is required to select from among numerous competing options. The goal of the decisionmaker is to select the option that will have the best future performance. This task is made difficult by the constraint that the decisionmaker has no way to predict the future performance of any of the options. Somewhat surprisingly, we find that the decisionmaker can still (at least in several important scenarios) pick a winner with high probability. Our result has several applications. For example, consider the problem of scheduling background jobs on a network of workstations (NOW) when very little is known about the future speed or availability of each workstation. In this problem, the goal is to schedule each job on a workstation which will have enough idle capacity to complete the job within a reasonable or ...
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 50 (9 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...
On the Influence of Lookahead in Competitive Paging Algorithms
 ALGORITHMICA
, 1997
"... We introduce a new model of lookahead for online paging algorithms and study several algorithms using this model. A paging algorithm is online with strong lookahead l if it sees the present request and a sequence of future requests that contains l pairwise distinct pages. We show that strong look ..."
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Cited by 37 (1 self)
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We introduce a new model of lookahead for online paging algorithms and study several algorithms using this model. A paging algorithm is online with strong lookahead l if it sees the present request and a sequence of future requests that contains l pairwise distinct pages. We show that strong lookahead has practical as well as theoretical importance and improves the competitive factors of online paging algorithms. This is the first model of lookahead having such properties. In addition to lower bounds we present a number of deterministic and randomized online paging algorithms with strong lookahead which are optimal or nearly optimal.
Frequency Allocation for WLANs Using Graph Colouring Techniques
 in Proceedings of the Second Annual Conference on Wireless Ondemand Network Systems and Services (WONS’05
"... At present, no standard frequency allocation mechanism exists for Wireless LAN access points. In this article, we introduce a number of techniques based on graph colouring algorithms, and demonstrate their effectiveness using simulations. We also suggest a preliminary message format the access poi ..."
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Cited by 18 (1 self)
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At present, no standard frequency allocation mechanism exists for Wireless LAN access points. In this article, we introduce a number of techniques based on graph colouring algorithms, and demonstrate their effectiveness using simulations. We also suggest a preliminary message format the access points could employ to exchange information regarding the wireless channel, and elaborate on the possible protocol architectures that could be used in the actual channel allocation process. 1.
A competitive analysis of the list update problem with lookahead
 Theoret. Comput. Sci
, 1998
"... We consider the question of lookahead in the list update problem: What improvement can be achieved in terms of competitiveness if an online algorithm sees not only the present request to be served but also some future requests? We introduce two different models of lookahead and study the list updat ..."
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Cited by 15 (0 self)
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We consider the question of lookahead in the list update problem: What improvement can be achieved in terms of competitiveness if an online algorithm sees not only the present request to be served but also some future requests? We introduce two different models of lookahead and study the list update problem using these models. We develop lower bounds on the competitiveness that can be achieved by deterministic online algorithms with lookahead. Furthermore we present online algorithms with lookahead that are competitive against static offline algorithms.
Online Independent Sets
"... . At each step of the online independent set problem, we are given a vertex v and its edges to the previously given vertices. We are to decide whether or not to select v as a member of an independent set. Our goal is to maximize the size of the independent set. It is not difficult to see that no ..."
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Cited by 12 (2 self)
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. At each step of the online independent set problem, we are given a vertex v and its edges to the previously given vertices. We are to decide whether or not to select v as a member of an independent set. Our goal is to maximize the size of the independent set. It is not difficult to see that no online algorithm can attain a performance ratio better than n 0 1, where n denotes the total number of vertices. Given this extreme difficulty of the problem, we study here relaxations where the algorithm can hedge his bets by maintaining multiple alternative solutions simultaneously. We introduce two models. In the first, the algorithm can maintain a polynomial number of solutions (independent sets) and choose the largest one as the final solution. We show that `( n log n ) is the best competitive ratio for this model. In the second more powerful model, the algorithm can copy intermediate solutions and grow the copied solutions in different ways. We obtain an upper bound of O(n...
Randomized Lower Bounds for Online Path Coloring
, 1998
"... We study the power of randomization in the design of online graph coloring algorithms. No specific network topology for which randomized online algorithms perform substantially better than deterministic algorithms is known until now. We present randomized lower bounds for online coloring of some ..."
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Cited by 7 (0 self)
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We study the power of randomization in the design of online graph coloring algorithms. No specific network topology for which randomized online algorithms perform substantially better than deterministic algorithms is known until now. We present randomized lower bounds for online coloring of some well studied network topologies. We show that no randomized algorithm for online coloring of interval graphs achieves a competitive ratio strictly better than the best known deterministic algorithm [KT81]. We also present a first lower bound on the competitive ratio of randomized algorithms for path coloring on tree networks, then answering an open question posed in [BEY98]. We prove an\Omega\Gamma/15 \Delta) lower bound for trees of diameter \Delta = O(log n) that compares with the known O(\Delta)competitive deterministic algorithm for the problem, then still leaving open the question if randomization helps for this specific topology. 1 Introduction In this paper we present random...
Parallel and Online Graph Coloring
"... We discover a surprising connection between graph coloring in two orthogonal paradigms: parallel and online computing. We present a randomized online coloring algorithm with a performance ratio of O(n = log n), an improvement of plog n factor over the previous best known algorithm of Vishwanathan. ..."
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Cited by 7 (3 self)
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We discover a surprising connection between graph coloring in two orthogonal paradigms: parallel and online computing. We present a randomized online coloring algorithm with a performance ratio of O(n = log n), an improvement of plog n factor over the previous best known algorithm of Vishwanathan. Also, from the same principles, we construct a parallel coloring algorithm with the same performance ratio, for the o/rst such result. As a byproduct, we obtain a parallel approximation for the independent set problem.
Delayed Information and Action in OnLine Algorithms
 39th IEEE symposium on Foundations of Computer Science
, 1998
"... Most online analysis assumes that, at each time step, all relevant information up to that time step is available and a decision has an immediate effect. In many online problems, however, the time relevant information is available and the time a decision has an effect may be decoupled. For example, ..."
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Cited by 6 (0 self)
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Most online analysis assumes that, at each time step, all relevant information up to that time step is available and a decision has an immediate effect. In many online problems, however, the time relevant information is available and the time a decision has an effect may be decoupled. For example, when making an investment, one might not have completely uptodate information on market prices. Similarly, a buy or sell order might only be executed some time later in the future. We introduce and explore natural delayed models for several wellknown online problems. Our analyses demonstrate the importance of considering timeliness in determining the competitive ratio of an online algorithm. For many problems, we demonstrate that there exist algorithms with small competitive ratios even when large delays affect the timeliness of information and the effect of decisions.