Maximum weight disjoint paths in outerplanar graphs via single-tree cut approximators

نویسندگان

چکیده

Since 1997 there has been a steady stream of advances for the maximum disjoint paths problem. Achieving tractable results usually required focusing on relaxations such as: (i) to allow some bounded edge congestion in solutions, (ii) only consider unit weight (cardinality) setting, (iii) require fractional routability selected demands (the all-or-nothing flow setting). For general form (no congestion, weights, integral routing) edge-disjoint (edp) even case capacity trees which are stars generalizes matching problem Edmonds provided an exact algorithm. capacitated trees, Garg, Vazirani, Yannakakis showed is APX-Hard and Chekuri, Mydlarz, Shepherd 4-approximation. This essentially setting where constant approximation known edp. We extend their result by giving constant-factor algorithm general-form edp outerplanar graphs. A key component find single-tree O(1) cut approximator Previously approximators were via distributions these based implicitly Gupta, Newman, Rabinovich Sinclair distance tree embeddings combined with Anderson Feige.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Maximum Edge-Disjoint Paths in k-Sums of Graphs

We consider the approximability of the maximum edge-disjoint paths problem (MEDP) in undirected graphs, and in particular, the integrality gap of the natural multicommodity flow based relaxation for it. The integrality gap is known to be Ω( √ n) even for planar graphs [14] due to a simple topological obstruction and a major focus, following earlier work [17], has been understanding the gap if s...

متن کامل

Intersection graphs of vertex disjoint paths in a tree

Two characterizations of intersection graphs of vertex disjoint paths in a tree, one in terms of maximal clique separator and the other in terms of minimal forbidden subgraphs, are presented. A polynomial recognition algorithm for this class is suggested.

متن کامل

New Algorithms for Maximum Disjoint Paths Based on Tree-Likeness

We study the classical NP-hard problems of finding maximum-size subsets from given sets of k terminal pairs that can be routed via edge-disjoint paths (MaxEDP) or node-disjoint paths (MaxNDP) in a given graph. The approximability of MaxEDP/NDP is currently not well understood; the best known lower bound is Ω(log1/2−ε n), assuming NP 6⊆ ZPTIME(n ). This constitutes a significant gap to the best ...

متن کامل

Maximum Disjoint Paths on Edge-Colored Graphs: Approximability and Tractability

The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate the approximation and parameterized complexity of the problem. First, we show that, for any constant ε > 0, the problem is not approximable within factor c1−ε, where c ...

متن کامل

On the maximum disjoint paths problem on edge-colored graphs

Motivated by applications to social network analysis (SNA), we study the problem of finding the maximum number of disjoint unicolor paths in an edge-colored graph. We show the NP-hardness and the approximability of the problem, and both approximation and exact algorithms are proposed. Since short paths are much more significant in SNA, we also study the length-bounded version of the problem, in...

متن کامل

ذخیره 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: Mathematical Programming

سال: 2022

ISSN: ['0025-5610', '1436-4646']

DOI: https://doi.org/10.1007/s10107-022-01780-0