Related papers: The Packed Interval Covering Problem is NP-complet…
The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric…
In this short note, we show two NP-completeness results regarding the \emph{simultaneous representation problem}, introduced by Lubiw and Jampani. The simultaneous representation problem for a given class of intersection graphs asks if some…
Every semicomplete multipartite digraph contains a quasi-Hamiltonian path, but the problem of finding a quasi-Hamiltonian path with prescribed start and end vertex is NP-complete even when restricted to semicomplete multipartite digraphs…
This paper deals with the problem of circle packing, in which the largest radii circle is to be fit in a confined space filled with arbitrary circles of different radii and centers. A circle packing problem is one of a variety of cutting…
We consider election scenarios with incomplete information, a situation that arises often in practice. There are several models of incomplete information and accordingly, different notions of outcomes of such elections. In one well-studied…
We intend to create new concepts aimed at finding necessary and sufficient conditions for Boolean satisfiability so that these conditions can be verified in polynomial time. Based on these conditions it will be possible to create an…
${ NP}$-complete problem "Hamiltonian cycle"\ for graph $G=(V,E)$ is extended to the "Hamiltonian Complement of the Graph"\ problem of finding the minimal cardinality set $H$ containing additional edges so that graph $G=(V,E\cup H)$ is…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…
Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel…
We claim to resolve the P=?NP problem via a formal argument for P=NP.
Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination problem), covering the vertex set by cliques (clique covering…
We introduce the maximum $n$-times coverage problem that selects $k$ overlays to maximize the summed coverage of weighted elements, where each element must be covered at least $n$ times. We also define the min-cost $n$-times coverage…
It is well-known that the Vertex Cover problem is in P on bipartite graphs, however; the computational complexity of the Partial Vertex Cover problem on bipartite graphs is open. In this paper, we first show that the Partial Vertex Cover…
We revisit the problem of computing an optimal partial cover of points by intervals. We show that the greedy algorithm computes a permutation $\Pi = \pi_1, \pi_2,\ldots$ of the intervals that is $3/4$-competitive for any prefix of $k$…
Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the…
In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…
Let $M$ be a real $r\times c$ matrix and let $k$ be a positive integer. In the column subset selection problem (CSSP), we need to minimize the quantity $\|M-SA\|$, where $A$ can be an arbitrary $k\times c$ matrix, and $S$ runs over all…
The purpose of this note is to attach a name to a natural class of combinatorial problems and to point out that this class includes many important special cases. We also show that a simple problem of placing nonoverlapping labels on a…
The well-known sequentially lifted cover inequality is widely employed in solving mixed integer programs. However, it is still an open question whether a sequentially lifted cover inequality can be computed in polynomial time for a given…