DeepAI AI Chat
Log In Sign Up

Maximum Weighted Matching with Few Edge Crossings for 2-Layered Bipartite Graph

by   Kazuya Haraguchi, et al.
National University Corporation Otaru University of Commerce

Let c denote a non-negative constant. Suppose that we are given an edge-weighted bipartite graph G=(V,E) with its 2-layered drawing and a family X of intersecting edge pairs. We consider the problem of finding a maximum weighted matching M* such that each edge in M* intersects with at most c other edges in M*, and that all edge crossings in M* are contained in X. In the present paper, we propose polynomial-time algorithms for the problem for c=1 and 2. The time complexities of the algorithms are O((k+m)log n) for c=1 and O(m^4log n+k^3+n(k^2+log n)) for c=2, respectively, where n=|V|, m=|E| and k=|X|.


page 1

page 2

page 3

page 4


A Simple 1-1/e Approximation for Oblivious Bipartite Matching

We study the oblivious matching problem, which aims at finding a maximum...

Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching

We present an auction algorithm using multiplicative instead of constan...

A Weighted Approach to the Maximum Cardinality Bipartite Matching Problem with Applications in Geometric Settings

We present a weighted approach to compute a maximum cardinality matching...

Finding Dominating Induced Matchings in S_1,1,5-Free Graphs in Polynomial Time

Let G=(V,E) be a finite undirected graph. An edge set E' ⊆ E is a domin...

Algorithms for the Euclidean Bipartite Edge Cover Problem

Given a graph G=(V,E) with costs on its edges, the minimum-cost edge cov...

Beating (1-1/e)-Approximation for Weighted Stochastic Matching

In the stochastic weighted matching problem, the goal is to find a large...

Neural Bipartite Matching

Graph neural networks have found application for learning in the space o...