ar X iv : 1 20 7 . 52 15 v 2 [ cs . D S ] 3 0 Ju l 2 01 2 Density Functions subject to a Co - Matroid Constraint ∗
نویسندگان
چکیده
In this paper we consider the problem of finding the densest subset subject to co-matroid constraints. We are given a monotone supermodular set function f defined over a universe U , and the density of a subset S is defined to be f(S)/|S|. This generalizes the concept of graph density. Comatroid constraints are the following: given matroidM a set S is feasible, iff the complement of S is independent in the matroid. Under such constraints, the problem becomes NP-hard. The specific case of graph density has been considered in literature under specific co-matroid constraints, for example, the cardinality matroid and the partition matroid. We show a 2-approximation for finding the densest subset subject to co-matroid constraints. Thus, for instance, we improve the approximation guarantees for the result for partition matroids in the literature.
منابع مشابه
On Integer Programming and the Path-width of the Constraint Matrix
We use the Exponential Time and Strong Exponential Time hypotheses (ETH & SETH) to provide conditional lower bounds on the solvability of the integer programming (IP) problem. We provide evidence that the running times of known pseudo-polynomial time algorithms solving IP, when the number of constraints is a constant [Papadimitriou, J. ACM 1981] and when the branch-width of the corresponding co...
متن کاملar X iv : 0 90 9 . 44 56 v 1 [ cs . A I ] 2 4 Se p 20 09 The Weighted C FG Constraint
We introduce the weighted CFG constraint and propose a propagation algorithm that enforces domain consistency in O(n|G|) time. We show that this algorithm can be decomposed into a set of primitive arithmetic constraints without hindering propagation.
متن کاملar X iv : h ep - l at / 0 01 20 10 v 1 7 D ec 2 00 0 1 The Vacuum Polarization : Power Corrections beyond OPE ? ∗
X iv :h ep -l at /0 01 20 10 v1 7 D ec 2 00 0 1 The Vacuum Polarization: Power Corrections beyond OPE ? ∗ M. Göckeler, R. Horsley, W. Kürzinger, V. Linke, D. Pleiter, P. E. L. Rakow and G. Schierholz Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany Deutsches Elektronen-Synchrotron DESY & NIC, D-15735 Zeuthen, Germany Institut für Physik, Humboldt-Universität...
متن کاملar X iv : h ep - e x / 97 06 01 7 v 1 2 3 Ju n 19 97 SLAC – PUB – 7567 June 1997
We review recent B physics results obtained in polarized e + e − interactions at the SLC by the SLD experiment. The excellent 3-D vertexing capabilities of SLD are exploited to extract precise B + and B 0 d lifetimes, as well as measurements of the time evolution of B 0 d − B 0 d mixing.
متن کامل