Related papers: The Packed Interval Covering Problem is NP-complet…
Given a property (graph class) $\Pi$, a graph $G$, and an integer $k$, the \emph{$\Pi$-completion} problem consists in deciding whether we can turn $G$ into a graph with the property $\Pi$ by adding at most $k$ edges to $G$. The…
The chromatic number of signed graphs is defined recently. The coloring and clique problem of interval graphs has been studied and polynomial time algorithms are established. Here we consider these problems for signed interval graphs and…
NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…
A polynomial algorithm is obtained for the NP-complete linear ordering problem.
We prove that the quiver problem is NP complete.
We show that the problem of deciding whether the vertex set of a graph can be covered with at most two bicliques is in NP$\cap$coNP. We thus almost determine the computational complexity of a problem whose status has remained open for quite…
In this paper, we settle the open complexity status of interval constrained coloring with a fixed number of colors. We prove that the problem is already NP-complete if the number of different colors is 3. Previously, it has only been known…
We present the first formal verification of approximation algorithms for NP-complete optimization problems: vertex cover, independent set, set cover, center selection, load balancing, and bin packing. We uncover incompletenesses in existing…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
We resolve the longstanding open problem concerning the computational complexity of Max Cut on interval graphs by showing that it is NP-complete.
We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete.
In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.
We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
We consider a variant of the path cover problem, namely, the $k$-fixed-endpoint path cover problem, or kPC for short, on interval graphs. Given a graph $G$ and a subset $\mathcal{T}$ of $k$ vertices of $V(G)$, a $k$-fixed-endpoint path…
We demonstrate a polynomial approach to express the decision version of the directed Hamiltonian Cycle Problem (HCP), which is NP-Complete, as the Solvability of a Polynomial Equation with a constant number of variables, within a bounded…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
In this paper we summarize the existing principles for building unconventional computing devices that involve delayed signals for encoding solutions to NP-complete problems. We are interested in the following aspects: the properties of the…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…