Weighted Triangle-free 2-matching Problem with Edge-disjoint Forbidden Triangles

11/15/2019
by   Yusuke Kobayashi, et al.
0

The weighted T-free 2-matching problem is the following problem: given an undirected graph G, a weight function on its edge set, and a set T of triangles in G, find a maximum weight 2-matching containing no triangle in T. When T is the set of all triangles in G, this problem is known as the weighted triangle-free 2-matching problem, which is a long-standing open problem. A main contribution of this paper is to give a first polynomial-time algorithm for the weighted T-free 2-matching problem under the assumption that T is a set of edge-disjoint triangles. In our algorithm, a key ingredient is to give an extended formulation representing the solution set, that is, we introduce new variables and represent the convex hull of the feasible solutions as a projection of another polytope in a higher dimensional space. Although our extended formulation has exponentially many inequalities, we show that the separation problem can be solved in polynomial time, which leads to a polynomial-time algorithm for the weighted T-free 2-matching problem.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/22/2018

Maximum Weight Independent Sets for (S_1,2,4,Triangle)-Free Graphs in Polynomial Time

The Maximum Weight Independent Set (MWIS) problem on finite undirected g...
research
01/27/2023

A Strongly Polynomial-Time Algorithm for Weighted General Factors with Three Feasible Degrees

General factors are a generalization of matchings. Given a graph G with ...
research
03/19/2020

Independent sets in (P_4+P_4,Triangle)-free graphs

The Maximum Weight Independent Set Problem (WIS) is a well-known NP-hard...
research
12/31/2020

A simple combinatorial algorithm for restricted 2-matchings in subcubic graphs – via half-edges

We consider three variants of the problem of finding a maximum weight re...
research
05/08/2023

In Honour of Ted Swart

This is a tribute to my dear life-long friend, mentor and colleague Ted ...
research
02/05/2020

Polygon Extraction from Triangular Meshes

This paper presents Polylidar, an efficient algorithm to extract non-con...
research
07/22/2019

Translating between the representations of a ranked convex geometry

It is well known that every closure system can be represented by an impl...

Please sign up or login with your details

Forgot password? Click here to reset