Online capacitated interval coloring

Authors:
Leah Epstein;Thomas Erlebach;Asaf Levin
Affiliations:
Department of Mathematics, University of Haifa, Haifa, Israel;Department of Computer Science, University of Leicester, England;Department of Statistics, The Hebrew University, Jerusalem, Israel
Venue:
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Year:
2007

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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 = mini ci. For the case bmax cmin, we give an algorithm with competitive ratio O(log bmax/cmin) 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.