Abstract:Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only "approximately" formulated for original real-world problems. To solve this issue, finding \emph{multiple} solutions is a natural direction, and diversity of solutions is an important concept in this context. Unfortunately, finding diverse solutions is much harder than finding a single solution. To cope with difficulty, we investigate the approximability of finding diverse solutions. As a main result, we propose a framework to design approximation algorithms for finding diverse solutions, which yields several outcomes including constant-factor approximation algorithms for finding diverse matchings in graphs and diverse common bases in two matroids and PTASes for finding diverse minimum cuts and interval schedulings.
From: Kazuhiro Kurita [view email]
[v1]
Sat, 22 Jan 2022 01:51:58 UTC (32 KB)
[v2]
Tue, 7 Jul 2026 22:58:50 UTC (35 KB)
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