Norito Minamikawa | Searcharxiv

arXiv2025

Computational Complexity and Integer Programming Formulation of the Oredango Puzzle

Oredango puzzle, one of the pencil puzzles, was originally created by Kanaiboshi and published in the popular puzzle magazine Nikoli. In this paper, we show NP- and ASP-completeness of Oredango by constructing a reduction from the 1-in-3SAT problem. Next, we formulate Oredango as an 0-1 integer-programming problem, and present numerical results obtained by solving Oredango puzzles from Nikoli and PuzzleSquare JP using a 0-1 optimization solver.

cs.CC↗

arXiv2022

Geodesic Property of Greedy Algorithms for Optimization Problems on Jump Systems and Delta-matroids

The concept of jump system, introduced by Bouchet and Cunningham (1995), is a set of integer points satisfying a certain exchange property. We consider the minimization of a separable convex function on a jump system. It is known that the problem can be solved by a greedy algorithm. In this paper, we are interested in whether the greedy algorithm has the geodesic property, which means that the trajectory of solution generated by the algorithm is a geodesic from the initial solution to a nearest optimal solution. We show that a special implementation of the greedy algorithm enjoys the geodesic property, while the original algorithm does not. As a corollary to this, we present a new greedy algorithm for linear optimization on a delta-matroid and show that the algorithm has the geodesic property.

math.OC↗