Algorithms for the Prize-Collecting $k$-Steiner Tree Problem
نویسندگان
چکیده
In this paper, we study the prize-collecting $k$ -Steiner tree ( xmlns:xlink="http://www.w3.org/1999/xlink">$\mathsf{PC}k\mathsf{ST}$ ) problem. We are given a graph xmlns:xlink="http://www.w3.org/1999/xlink">$G=(V, E)$ and an integer . The is connected undirected. A vertex xmlns:xlink="http://www.w3.org/1999/xlink">$r\in V$ called root subset xmlns:xlink="http://www.w3.org/1999/xlink">$R\subseteq terminals also given. feasible solution for xmlns:xlink="http://www.w3.org/1999/xlink">$F$ rooted at xmlns:xlink="http://www.w3.org/1999/xlink">$r$ connecting least vertices in xmlns:xlink="http://www.w3.org/1999/xlink">$R$ Excluding from incurs penalty cost, including edge cost. wish to find with minimum total cost of sum costs edges not present simple approximation algorithm ratio 5.9672 This uses algorithms Steiner (PCST) problem xmlns:xlink="http://www.w3.org/1999/xlink">$k\mathsf{ST}$ as subroutines. Then propose primal-dual based improve 5.
منابع مشابه
The Prize Collecting Steiner Tree Problem
This work is motivated by an application in local access network design that can be modeled using the KP-hard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primal-dual 2-approximation algorithm devised for it by Goemans and Williamson. We develop several modifications to the algorithm which lead to theoretical as well as practical improvements in...
متن کاملElementary Approximation Algorithms for Prize Collecting Steiner Tree Problems
This paper deals with approximation algorithms for the prize collecting generalized Steiner forest problem, defined as follows. The input is an undirected graph G= (V ,E), a collection T = {T1, . . . , Tk}, each a subset of V of size at least 2, a weight function w :E → R+, and a penalty function p :T → R+. The goal is to find a forest F that minimizes the cost of the edges of F plus the penalt...
متن کاملSolving the Prize-Collecting Steiner Tree Problem to Optimality
The Prize-Collecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears in the design of utility networks (eg. fiber optics or district heating) where profit generating customers and the network connecting the...
متن کاملThe Fractional Prize-Collecting Steiner Tree Problem on Trees
We consider the fractional prize-collecting Steiner tree problem on trees. This problem asks for a subtree T containing the root of a given tree G = (V, E) maximizing the ratio of the vertex profits P v∈V (T ) p(v) and the edge costs P e∈E(T ) c(e) plus a fixed cost c0 and arises in energy supply management. We experimentally compare three algorithms based on parametric search: the binary searc...
متن کاملPrimal-dual approximation algorithms for the Prize-Collecting Steiner Tree Problem
The primal-dual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2−1/(n−1))-approximation for the Prize-Collecting Steiner Tree Problem that runs in O(n3 logn) time—it applies the primaldual scheme once for each of the n vertices of the graph. We present a primal-dual algorithm that runs in O(n2 logn), as it applies this scheme only once...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tsinghua Science & Technology
سال: 2022
ISSN: ['1878-7606', '1007-0214']
DOI: https://doi.org/10.26599/tst.2021.9010053