Improved approximations of crossings in graph drawings
Guy Even, Sudipto Guha, et al.
STOC 2000
Let G = (V, E) be a weighted undirected graph where all weights are at least one. We consider the following generalization of feedback set problems. Let S ⊂ V be a subset of the vertices. A cycle is called interesting if it intersects the set S. A subset feedback edge (vertex) set is a subset of the edges (vertices) that intersects all interesting cycles. In minimum subset feedback problems the goal is to find such sets of minimum weight. This problem has a variety of applications, among them genetic linkage analysis and circuit testing. The case in which S consists of a single vertex is equivalent to the multiway cut problem, in which the goal is to separate a given set of terminals. Hence, the subset feedback problem is NP-complete and also generalizes the multiway cut problem. We provide a polynomial time algorithm for approximating the subset feedback edge set problem that achieves an approximation factor of two. This implies a Δ-approximation algorithm for the subset feedback vertex set problem, where Δ is the maximum degree in G. We also consider the multicut problem and show how to achieve an O(log τ*) approximation factor for this problem, where τ* is the value of the optimal fractional solution. To achieve the O(log τ*) factor we employ a bootstrapping technique.
Guy Even, Sudipto Guha, et al.
STOC 2000
Miriam Allalouf, Gidon Gershinsky, et al.
SmartGridComm 2011
Guy Even, Ilan Y. Spillinger, et al.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Pankaj K. Agarwal, Alok Aggarwal, et al.
Discrete Applied Mathematics