Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
On chromatic sums and distributed resource allocation
Information and Computation
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Approximating the domatic number
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Adaptive ordering of pipelined stream filters
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Packet classification in large ISPs: design and evaluation of decision tree classifiers
SIGMETRICS '05 Proceedings of the 2005 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Associative search in peer to peer networks: Harnessing latent semantics
Computer Networks: The International Journal of Computer and Telecommunications Networking
A constant factor approximation algorithm for generalized min-sum set cover
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Improved bounds for sum multicoloring and scheduling dependent jobs with minsum criteria
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
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The input to the min sum set cover problem is a collection of n sets that jointly cover m elements. The output is a linear order on the sets, namely, in every time step from 1 to n exactly one set is chosen. For every element, this induces a first time step by which it is covered. The objective is to find a linear arrangement of the sets that minimizes the sum of these first time steps over all elements.We show that a greedy algorithm approximates min sum set cover within a ratio of 4. This result was implicit in work of Bar-Noy, Bellare, Halldorsson, Shachnai and Tamir (1998) on chromatic sums, but we present a simpler proof. We also show that for every 驴 0, achieving an approximation ratio of 4 - 驴 is NP-hard. For the min sum vertex cover version of the problem, we show that it can be approximated within a ratio of 2, and is NP-hard to approximate within some constant 驴 1.