The partial representation extension problem, introduced by Klav́ık et al. (2011), generalizes the recognition problem. In this short note we show that this problem is NP-complete for unit circular-arc graphs.

The Equal Sum Subsets problem, where we are given a set of positive integers and we ask for two nonempty disjoint subsets such that their elements add up to the same total, is known to be NP-hard. In this paper we give (pseudo-)polynomial algorithms and/or (strong) NP-hardness proofs for several natural variations of Equal Sum Subsets. Among others we present (1) a framework for obtaining NP-ha...

Film is a “closed” medium, so narrative closure is a necessity; VR is a “wideness” medium, so narrative completeness is not vital. In this paper, we would like to analyse the purposes of narrative film closure in terms of the viewer and explore VR “wideness” effects within user emotions, to demonstrate that “wideness” eliminates the necessity of closure through continuous engagement and gratifi...

Polynomially solvable NP-hard pseudopolynomially solvable Strongly NP-hard P M j , p j = 1 Cmax R M j , pmtn ∗ Cmax P2 |M j | = 2 Cmax Pm |M j | = 2 Cmax Rm M j Cmax P |M j | = 2 Cmax

The partial inverse minimum cut problem is to minimally modify the capacities of a digraph such that there exists a minimum cut with respect to the new capacities that contains all arcs of a prespecified set. Orlin showed that the problem is strongly NP-hard if the amount of modification is measured by the weighted L1-norm. We prove that the problem remains hard for the unweighted case and show...

We prove that it is NP-complete to decide whether a given string can be factored into palindromes that are each unique in the factorization.

We show NP-completeness for the recognition problem of classical 2-

Bill Lawvere’s 1973 milestone paper “Metric spaces, generalized logic, and closed categories” helped us to detect categorical structures in previously unexpected surroundings. His revolutionary idea was not only to regard individual metric spaces as categories (enriched over the monoidal-closed category given by the non-negative extended real half-line, with arrows provided by ≥ and tensor by +...