The year 2012 marks the 40th anniversary of the publication of the influential paper “Reducibility among combinatorial problems” by Richard Karp [37]. This paper was the first to demonstrate the wide applicability of the concept now known as NP-completeness, which had been introduced the previous year by Stephen Cook and Leonid Levin, independently. 2012 also marks the 100th anniversary of the ...

This paper follows the methodology introduced by Agrawal and Biswas in [AB92], based on a notion of universality for the relations associated with NP-complete problems. The purpose was to study NP-complete problems by examining the effects of reductions on the solution sets of the associated witnessing relations. This provided a useful criterion for NP-completeness while suggesting structural s...

Considering the contention for communication resources in task scheduling is discussed in [3]. Theorem 1 of [3] states the NP-completeness of the associated decision problem and the corresponding proof shows NP-completeness in the weak sense [2]. Here, a new proof is presented for Theorem 1 of [3] that shows NP-completeness in the strong sense. The proof is based on a reduction from the well-kn...

We investigate here the computational complexity of three natural problems in directed acyclic graphs. We prove their NP Completeness and consider their restrictions to linear orders.

In this paper we describe a family of open questions concerning strong completeness properties associated with the Baire Category Theorem. Some of our questions deal with classical completeness topics such as de Groot’s subcompactness property and the property now called Choquet completeness, while others ask about more recent topics such as domain-representability and its relation to classical...

We consider an integer-subset representation problem motivated by a medical application in radiation therapy. We prove NP-completeness, derive nontrivial bounds, and report on the performance of a greedy heuristic.

We sharpen the result that polarity and monopolarity are NP-complete problems by showing that they remain NP-complete if the input graph is restricted to be a 3-colourable comparability graph. We start by presenting a construction reducing 1-3-SAT to monopolarity of 3-colourable comparability graphs. Then we show that polarity is at least as hard as monopolarity for input graphs restricted to a...

A paper by Deng and Conitzer in AAAI’17 introduces disarmament games, in which players alternatingly commit not to play certain pure strategies. However, in practice disarmament usually does not consist in removing a strategy, but rather in removing a resource (and doing so rules out all the strategies in which that resource is used simultaneously). In this paper, we introduce a model of disarm...

In this note, we prove NP-completeness of the following problem: Given a set of trams of diierent types, which are stacked on sidings in their depot and an order in which trams of speciied types are supposed to leave. Is there an assignment of trams to departure times without any shunting movements? In the particular case where the number of sidings is xed, the problem is solvable in polynomial...

We study the complexity of expressing the greatest common divisor of n positive numbers as a linear combination of the numbers. We prove the NP-completeness of finding an optimal set of multipliers with respect to either the L0 metric or the L∞ norm. We present and analyze a new method for expressing the gcd of n numbers as their linear combination and give an upper bound on the size of the lar...