Efficient on-line algorithms for maintaining k-cover of sparse bit-strings


We consider the on-line problem of representing a sparse bit string by a set of k intervals, where k is much smaller than the length of the string. The goal is to minimize the total length of these intervals under the condition that each 1-bit must be in one of these intervals. We give an efficient greedy algorithm which takes time O(log k) per update (an update involves converting a 0-bit to a 1-bit), which is independent of the size of the entire string. We prove that this greedy algorithm is 2-competitive. We use a natural linear programming relaxation for this problem, and analyze the algorithm by finding a dual feasible solution whose value matches the cost of the greedy algorithm. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems

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@inproceedings{Kumar2012EfficientOA, title={Efficient on-line algorithms for maintaining k-cover of sparse bit-strings}, author={Amit Kumar and Preeti Ranjan Panda and Smruti R. Sarangi}, year={2012} }