Related papers: NP-hardness of hypercube 2-segmentation
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
We consider the popular matching problem in a roommates instance with strict preference lists. While popular matchings always exist in a bipartite instance, they need not exist in a roommates instance. The complexity of the popular matching…
IV-matching is a generalization of perfect bipartite matching. The complexity of finding IV-matching in a graph was posted as an open problem at the ICALP 2014 conference. In this note, we resolve the question and prove that, contrary to…
We show that P2T - the problem of deciding whether the edge set of a simple graph can be partitioned into two trees or not - is NP-complete.
In part I we reduced the arithmetic (characteristic zero) version of the P \not \subseteq NP conjecture to the problem of showing that a variety associated with the complexity class NP cannot be embedded in the variety associated the…
We show NP-completeness for the recognition problem of 2-line-bend graphs.
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…
The graph packing problem is a well-known area in graph theory. We consider a bipartite version and give almost tight conditions on the packability of two bipartite sequences.
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…
Two decision problems related to the computation of stopping sets in Tanner graphs are shown to be NP-complete. NP-hardness of the problem of computing the stopping distance of a Tanner graph follows as a consequence
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…
This extended abstract presents an overview on NP-hard optimization problems with multiple interdependent components. These problems occur in many real-world applications: industrial applications, engineering, and logistics. The fact that…
We resolve the longstanding open problem concerning the computational complexity of Max Cut on interval graphs by showing that it is NP-complete.
We present a template for the Promise Constraint Satisfaction Problem (PCSP) which is NP-hard but does not satisfy the current state-of-the-art hardness condition [ACMTCT'21]. We introduce a new "injective" condition based on the smooth…
Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki…
In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable…
An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually…
We show that the problem of finding a set with maximum cohesion in an undirected network is NP-hard.
Block Sorting is a well studied problem, motivated by its applications in Optical Character Recognition (OCR), and Computational Biology. Block Sorting has been shown to be NP-Hard, and two separate polynomial time 2-approximation…