An improved algorithm for online coloring of intervals with bandwidth

Azar, Yossi; Fiat, Amos; Levy, Meital; Narayanaswamy, N. S.

doi:10.1016/j.tcs.2006.06.014

Cited by 17 publications

(22 citation statements)

References 4 publications

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“…These are not necessarily the best algorithms for the problem. Narayanaswamy [Narayanaswamy 2004;Azar et al 2006] presented an algorithm that is 10-competitive for this problem, and this is the best bound known.…”

Section: Online Coloring Of Intervals With Bandwidthmentioning

confidence: 99%

Max-coloring and online coloring with bandwidths on interval graphs

Pemmaraju

Raman

Varadarajan

2011

ACM Trans. Algorithms

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Given a graph G = (V, E) and positive integral vertex weights w : V → N, the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C 1 , C 2 , . . . , C k , minimizemax v∈C i w(v). This problem, restricted to interval graphs, arises whenever there is a need to design dedicated memory managers that provide better performance than the general purpose memory management of the operating system.Though this problem seems similar to the dynamic storage allocation problem, there are fundamental differences. We make a connection between max-coloring and on-line graph coloring and use this to devise a simple 2-approximation algorithm for max-coloring on interval graphs. We also show that a simple first-fit strategy, that is a natural choice for this problem, yields an 8-approximation algorithm. We show this result by proving that the first-fit algorithm for on-line coloring an interval graph G uses no more than 8 · χ(G) colors, significantly improving the bound of 26·χ(G) by Kierstead and Qin (Discrete Math., 144, 1995). We also show that the max-coloring problem is NP-hard.The problem of online coloring of intervals with bandwidths is a simultaneous generalization of online interval coloring and online bin packing. The input is a set I of intervals, each interval i ∈ I having an associated bandwidth b(i) ∈ (0, 1]. We seek an online algorithm that produces a coloring of the intervals such that for any color c and any real r, the sum of the bandwidths of intervals containing r and colored c is at most 1. Motivated by resource allocation problems, Adamy and Erlebach (Proceedings of the First International Workshop on Online and Approximation Algorithms, 2003, LNCS 2909, pp 1-12 ) consider this problem and present an algorithm that uses at most 195 times the number of colors used by an optimal off-line algorithm. Using the new analysis of first-fit coloring of interval graphs, we show that the Adamy-Erlebach algorithm is 35-competitive. Finally, we generalize the Adamy-Erlebach algorithm to a class of algorithms and show that a different instance from this class is 30-competitive.

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Section: Online Coloring Of Intervals With Bandwidthmentioning

confidence: 99%

Max-coloring and online coloring with bandwidths on interval graphs

Pemmaraju

Raman

Varadarajan

2011

ACM Trans. Algorithms

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“…This constraint must hold for each of the d components For an interval I, This algorithm has competitive ratios of 4, 3 and 3 for the classes S 1 , S 2 and S 3 , respectively. Since we run in parallel d instances of the algorithm of [2], each of which has a competitive ratio of at most 10, we get the combined competitive ratio of at most 10d.…”

Section: Coloring With Vector Constraintsmentioning

confidence: 99%

Online Interval Coloring with Packing Constraints

Epstein

Levy

2005

Mathematical Foundations of Computer Science 2005

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Abstract. We study online interval coloring problems with bandwidth. We are interested in some variants motivated by bin packing problems. Specifically we consider open-end coloring, cardinality constrained coloring, coloring with vector constraints and finally a combination of both the cardinality and the vector constraints. We construct competitive algorithms for each of the variants. Additionally, we present a lower bound of 24/7 for interval coloring with bandwidth, which holds for all the above models, and improves the current lower bound for the standard interval coloring with bandwidth problem.

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“…They presented an online algorithm with a competitive ratio of at most 195. Azar et al [2] presented a new algorithm with a competitive ratio of 10. In [9] we studied several extensions of this problem including coloring of unit length intervals.…”

Section: Introductionmentioning

confidence: 99%

“…We use ideas which are extensions of the algorithm in [2]. For the open-end coloring model we present an algorithm with competitive ratio of at most 12.…”

Section: Introductionmentioning

confidence: 99%

Online interval coloring with packing constraints

Epstein

Levy

2008

Theoretical Computer Science

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a b s t r a c tWe study online interval coloring problems with bandwidth. We are interested in some variants motivated by bin packing problems. Specifically we consider open-end coloring, cardinality constrained coloring, coloring with vector constraints and finally a combination of both the cardinality and the vector constraints. We construct competitive algorithms for each of the variants. Additionally, we present a lower bound of 24/7 for interval coloring with bandwidth, which holds for all the above models, and improves the current lower bound for the standard interval coloring with bandwidth problem.

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An improved algorithm for online coloring of intervals with bandwidth

Cited by 17 publications

References 4 publications

Max-coloring and online coloring with bandwidths on interval graphs

Max-coloring and online coloring with bandwidths on interval graphs

Online Interval Coloring with Packing Constraints

Online interval coloring with packing constraints

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