David Könen

Output-sensitive complexity of multiobjective combinatorial optimization

Journal of Multi-Criteria Decision Analysis, 2017

We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization... more We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is output-sensitive, i.e., its running time is bounded by a polynomial in the input and the output size. We provide both practical examples of MOCO problems for which such an efficient algorithm exists as well as problems for which no efficient algorithm exists under mild complexity theoretic assumptions.

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Finding all minimum cost flows and a faster algorithm for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e636" altimg="si10.svg"><mml:mi>K</mml:mi></mml:math> best flow problem

Discrete Applied Mathematics, Nov 1, 2022

An output-polynomial time algorithm to determine all supported efficient solutions for multi-objective integer network flow problems

arXiv (Cornell University), May 22, 2023

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Finding all minimum cost flows and a faster algorithm for the K best flow problem

ArXiv, 2021

This paper addresses the problem of determining all optimal integer solutions of a linear integer... more This paper addresses the problem of determining all optimal integer solutions of a linear integer network flow problem, which we call the all optimal integer flow (AOF) problem. We derive an O(F (m+ n) +mn+M) time algorithm to determine all F many optimal integer flows in a directed network with n nodes and m arcs, where M is the best time needed to find one minimum cost flow. We remark that stopping Hamacher’s well-known method for the determination of the K best integer flows [11] at the first sub-optimal flow results in an algorithm with a running time of O(Fm(n logn+m) +M) for solving the AOF problem. Our improvement is essentially made possible by replacing the shortest path sub-problem with a more efficient way to determine a so-called proper zero cost cycle using a modified depth-first search technique. As a byproduct, our analysis yields an enhanced algorithm to determine the K best integer flows that runs in O(Kn3 +M). Besides, we give lower and upper bounds for the number ...

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