Minimum Activation Cost Edge-Disjoint Paths in Graphs with Bounded Tree-Width
نویسندگان
چکیده
In activation network problems we are given a directed or undirected graph G = (V,E) with a family {fuv : (u, v) ∈ E} of monotone non-decreasing activation functions from D to {0, 1}, where D is a constant-size subset of the non-negative real numbers, and the goal is to find activation values xv for all v ∈ V of minimum total cost ∑ v∈V xv such that the activated set of edges satisfies some connectivity requirements. We propose algorithms that optimally solve the minimum activation cost of k node-disjoint st-paths (st-MANDP) problem in O(tw((5 + tw)|D|)|V |) time and the minimum activation cost of node-disjoint paths (MANDP) problem for k disjoint terminal pairs (s1, t1), . . . , (sk, tk) in O(tw((4 + 3tw)|D|)|V |) time for graphs with treewidth bounded by tw.
منابع مشابه
Edge Disjoint Paths and Multicut Problems in Graphs Generalizing the Trees∗
We generalize all the results obtained for maximum integer multiflow and minimum multicut problems in trees by Garg et al. [Primaldual approximation algorithms for integral flow and multicut in trees. Algorithmica 18 (1997) 3–20] to graphs with a fixed cyclomatic number, while this cannot be achieved for other classical generalizations of the trees. Moreover, we prove that the minimum multicut ...
متن کاملClique-width: When Hard Does Not Mean Impossible
In recent years, the parameterized complexity approach has lead to the introduction of many new algorithms and frameworks on graphs and digraphs of bounded clique-width and, equivalently, rank-width. However, despite intensive work on the subject, there still exist well-established hard problems where neither a parameterized algorithm nor a theoretical obstacle to its existence are known. Our a...
متن کاملActivation network problems
Network design problems traditionally are modelled by a graph where each edge (or node) has a fixed cost. We investigate optimization problems in a realistic model for wireless network design called activation network. The activation network setting can be defined as follows. We are given a directed or undirected graph G = (V,E) together with a family {fuv : (u, v) ∈ E} of monotone nondecreasin...
متن کاملThe Minimum Vulnerability Problem on Graphs
Suppose that each edge e of an undirected graph G is associated with three nonnegative integers cost(e), vul(e) and cap(e), called the cost, vulnerability and capacity of e, respectively. Then, we consider the problem of finding k paths in G between two prescribed vertices with the minimum total cost; each edge e can be shared without cost by at most vul(e) paths, and can be shared by more than...
متن کاملApproximation Algorithms for Disjoint st-Paths with Minimum Activation Cost
In network activation problems we are given a directed or undirected graph G = (V,E) with a family {fuv (xu, xv) : (u, v) ∈ E} of monotone non-decreasing activation functions from D to {0, 1}, where D is a constant-size domain. The goal is to find activation values xv for all v ∈ V of minimum total cost ∑ v∈V xv such that the activated set of edges satisfies some connectivity requirements. Netw...
متن کامل