Online capacitated interval coloring

Leah Epstein; Thomas Erlebach; Asaf Levin

doi:10.1007/978-3-540-74450-4_22

Online capacitated interval coloring

Leah Epstein, Thomas Erlebach, Asaf Levin

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In the online capacitated interval coloring problem, a sequence of requests arrive online. Each of the requests is an interval I_j ⊆{1,2,..., n} with bandwidth b_j. Initially a vector of capacities (c₁,C₂,..., C_n) is given. Each color can support a set of requests such that the total bandwidth of intervals containing i is at most c_i. The goal is to color the requests using a minimum number of colors. We present a constant competitive algorithm for the case where the maximum bandwidth b_max = max_j b_j is at most the minimum capacity c_min = min₁ c _i. For the case b_max > c_min, we give an algorithm with competitive ratio 0(log c_minb_max) and, using resource augmentation, a constant competitive algorithm. We also give a lower bound showing that constant competitive ratio cannot be achieved in this case without resource augmentation.

Original language	English
Title of host publication	Combinatorics, Algorithms, Probabilistic and Experimental Methodologies - First International Symposium, ESCAPE 2007, Revised Selected Papers
Publisher	Springer Verlag
Pages	243-254
Number of pages	12
ISBN (Print)	9783540744498
DOIs	https://doi.org/10.1007/978-3-540-74450-4_22
State	Published - 2007
Event	1st International Symposium on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies, ESCAPE 2007 - Hangzhou, China Duration: 7 Apr 2007 → 9 Apr 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4614 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	1st International Symposium on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies, ESCAPE 2007
Country/Territory	China
City	Hangzhou
Period	7/04/07 → 9/04/07

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-74450-4_22

Cite this

Epstein, L., Erlebach, T., & Levin, A. (2007). Online capacitated interval coloring. In Combinatorics, Algorithms, Probabilistic and Experimental Methodologies - First International Symposium, ESCAPE 2007, Revised Selected Papers (pp. 243-254). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4614 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-74450-4_22

Epstein, Leah ; Erlebach, Thomas ; Levin, Asaf. / Online capacitated interval coloring. Combinatorics, Algorithms, Probabilistic and Experimental Methodologies - First International Symposium, ESCAPE 2007, Revised Selected Papers. Springer Verlag, 2007. pp. 243-254 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In the online capacitated interval coloring problem, a sequence of requests arrive online. Each of the requests is an interval Ij ⊆{1,2,..., n} with bandwidth bj. Initially a vector of capacities (c1,C2,..., Cn) is given. Each color can support a set of requests such that the total bandwidth of intervals containing i is at most ci. The goal is to color the requests using a minimum number of colors. We present a constant competitive algorithm for the case where the maximum bandwidth bmax = maxj bj is at most the minimum capacity cmin = min1 c i. For the case bmax > cmin, we give an algorithm with competitive ratio 0(log cminbmax) and, using resource augmentation, a constant competitive algorithm. We also give a lower bound showing that constant competitive ratio cannot be achieved in this case without resource augmentation.",

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Epstein, L, Erlebach, T & Levin, A 2007, Online capacitated interval coloring. in Combinatorics, Algorithms, Probabilistic and Experimental Methodologies - First International Symposium, ESCAPE 2007, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4614 LNCS, Springer Verlag, pp. 243-254, 1st International Symposium on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies, ESCAPE 2007, Hangzhou, China, 7/04/07. https://doi.org/10.1007/978-3-540-74450-4_22

Online capacitated interval coloring. / Epstein, Leah; Erlebach, Thomas; Levin, Asaf.
Combinatorics, Algorithms, Probabilistic and Experimental Methodologies - First International Symposium, ESCAPE 2007, Revised Selected Papers. Springer Verlag, 2007. p. 243-254 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4614 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Levin, Asaf

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AB - In the online capacitated interval coloring problem, a sequence of requests arrive online. Each of the requests is an interval Ij ⊆{1,2,..., n} with bandwidth bj. Initially a vector of capacities (c1,C2,..., Cn) is given. Each color can support a set of requests such that the total bandwidth of intervals containing i is at most ci. The goal is to color the requests using a minimum number of colors. We present a constant competitive algorithm for the case where the maximum bandwidth bmax = maxj bj is at most the minimum capacity cmin = min1 c i. For the case bmax > cmin, we give an algorithm with competitive ratio 0(log cminbmax) and, using resource augmentation, a constant competitive algorithm. We also give a lower bound showing that constant competitive ratio cannot be achieved in this case without resource augmentation.

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Epstein L, Erlebach T, Levin A. Online capacitated interval coloring. In Combinatorics, Algorithms, Probabilistic and Experimental Methodologies - First International Symposium, ESCAPE 2007, Revised Selected Papers. Springer Verlag. 2007. p. 243-254. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-74450-4_22

Online capacitated interval coloring

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