Bounded Degree Group Steiner Tree Problems

Guy Kortsarz, Zeev Nutov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Motivated by some open problems posed in [13], we study three problems that seek a low degree subtree T of a graph G =(V, E). In the Min-Degree Group Steiner Tree problem we are given a collection of node subsets (groups), and T should contain a node from every group. In the Min-Degree Steiner k-Tree problem we are given a set R of terminals and an integer k, and T should contain k terminals. In both problems the goal is to minimize the maximum degree of T . In the more general Degrees Bounded Min-Cost Group Steiner Tree problem, we are also given edge costs and individual degree bounds (Formula Presented). The output tree T should obey the degree constraints degT (v) ≤ bv for all (Formula Presented), and among all such trees we seek one of minimum cost. When the input is a tree, an O(log2 n) approximation for the cost is given in [10]. Our first result generalizes [10] – we give a bicriteria (O(log2 n), O(log2 n))-approximation algorithm for Degrees Bounded Min-Cost Group Steiner Tree problem on tree inputs. This matches the cost ratio of [10] but also approximates the degrees within O(log2 n). Our second result shows that if Min-Degree Group Steiner Tree admits ratio ρ then Min-Degree Steiner k-Tree admits ratio ρ · O(log k). Combined with [12], this implies an O(log3 n)-approximation for Min-Degree Steiner k-Tree on general graphs, in quasi-polynomial time. Our third result is a polynomial time O(log3 n)-approximation algorithm for Min-Degree Group Steiner Tree on bounded treewidth graphs.

Original language English Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings Leszek Gasieniec, Leszek Gasieniec, Ralf Klasing, Tomasz Radzik Springer 343-354 12 9783030489656 https://doi.org/10.1007/978-3-030-48966-3_26 Published - 2020 31st International Workshop on Combinatorial Algorithms, IWOCA 2020 - Bordeaux, FranceDuration: 8 Jun 2020 → 10 Jun 2020

Publication series

Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 12126 LNCS 0302-9743 1611-3349

Conference

Conference 31st International Workshop on Combinatorial Algorithms, IWOCA 2020 France Bordeaux 8/06/20 → 10/06/20