핵심 개념
Geometric many-to-many matching problem solved with a near-linear approximation scheme.
초록
The content discusses a novel (1 + ε)-approximation algorithm for geometric many-to-many matching in any fixed dimension. It introduces the problem, presents prior research, and details the proposed solution. The algorithm achieves optimal running time and works under any Lp-norm. The paper outlines reductions, grid techniques, and algorithms used to solve the problem efficiently.
Introduction
Geometric matching in computational geometry
Optimization problems on edge-weighted geometric graphs
Matching-Related Problems
Applications in various fields
Bipartite and complete settings for matching problems
Minimum-Weight Perfect Matching
Variants like many-to-many matching
Reductions and algorithms for solving the problem
Preliminaries
Basic notations and definitions
Grids and data structures used
Approximation Scheme
Reductions to well-structured subproblems
Integer linear programming and FPT algorithm implementation
Conclusion and Open Questions
Summary of results and future research directions
통계
최적 실행 시간 Oε(n log n)에 대한 최적 근사 알고리즘
O(n log n) 시간에 대한 근사 알고리즘
Oε(n log n) 시간에 대한 근사 알고리즘
인용구
"Geometric matching is an important topic in computational geometry."
"The algorithm exploits the nice structures of the many-to-many matching problem itself."