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

Norito Minamikawa

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arXiv · 2206.10439

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

Norito Minamikawa

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Abstract

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.

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Norito Minamikawa. 2022-06-21. Geodesic Property of Greedy Algorithms for Optimization Problems on Jump Systems and Delta-matroids. https://arxiv.org/abs/2206.10439

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