TY - GEN

T1 - Ranking with submodular valuations

AU - Azar, Yossi

AU - Gamzu, Iftah

PY - 2011

Y1 - 2011

N2 - We study the problem of ranking with submodular valuations. An instance of this problem consists of a ground set [m], and a collection of n monotone sub-modular set functions f1,... fn, where each function fi : 2[m] → ℝ+. An additional input ingredient is a weight vector ω ∈ ℝ+n. The goal is to find a linear ordering of the ground set elements that minimizes the weighted cover time of the functions. The cover time of a function is the minimal number of elements in the prefix of the linear ordering that form a set whose corresponding function value is greater than a unit threshold value. Our main result is an O(ln(l/ε))-approximation algorithm for the problem, where e is the smallest nonzero marginal value that any function may gain from some element. Our algorithm orders the elements using an adaptive residual updates scheme, which may be of independent interest. We also prove that the problem is Ω(ln(l/ε))-hard to approximate, unless P = NP. This implies that the outcome of our algorithm is optimal up to constant, factors.

AB - We study the problem of ranking with submodular valuations. An instance of this problem consists of a ground set [m], and a collection of n monotone sub-modular set functions f1,... fn, where each function fi : 2[m] → ℝ+. An additional input ingredient is a weight vector ω ∈ ℝ+n. The goal is to find a linear ordering of the ground set elements that minimizes the weighted cover time of the functions. The cover time of a function is the minimal number of elements in the prefix of the linear ordering that form a set whose corresponding function value is greater than a unit threshold value. Our main result is an O(ln(l/ε))-approximation algorithm for the problem, where e is the smallest nonzero marginal value that any function may gain from some element. Our algorithm orders the elements using an adaptive residual updates scheme, which may be of independent interest. We also prove that the problem is Ω(ln(l/ε))-hard to approximate, unless P = NP. This implies that the outcome of our algorithm is optimal up to constant, factors.

UR - http://www.scopus.com/inward/record.url?scp=79955726089&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973082.81

DO - 10.1137/1.9781611973082.81

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AN - SCOPUS:79955726089

SN - 9780898719932

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1070

EP - 1079

BT - Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011

PB - Association for Computing Machinery

ER -