Related papers: The Complexity of Finding Tangles
A pattern p (i.e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of p by terminal words. The respective matching problem, i.e., deciding whether or not a given pattern…
Discrete tomography deals with reconstructing finite spatial objects from lower dimensional projections and has applications for example in timetable design. In this paper we consider the problem of reconstructing a tile packing from its…
We investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both sides is the preserved (the variables can be, however, separated…
We prove that certain problems naturally arising in knot theory are NP--hard or NP--complete. These are the problems of obtaining one diagram from another one of a link in a bounded number of Reidemeister moves, determining whether a link…
The computational complexity of tiling finite simply connected regions with a fixed set of tiles is studied in this paper. We show that the problem of tiling simply connected regions with a fixed set of $23$ Wang tiles is NP-complete. As a…
Time-evolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one…
Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths…
Deciding the existence of an $l\times m\times n$ integer threeway table with given line-sums is NP-complete already for fixed $l=3$, but is in P with both $l,m$ fixed. Here we consider {\em huge} tables, where the variable dimension $n$ is…
The present work proves that P=NP. The proof, presented in this work, is a constructive one: the program of a polynomial time deterministic multi-tape Turing machine M_ExistsAcceptingPath, that determines if there exists an accepting…
We prove that it is NP-hard to decide whether two points in a polygonal domain with holes can be connected by a wire. This implies that finding any approximation to the shortest path for a long snake amidst polygonal obstacles is NP-hard.…
We investigate the computational complexity of the following problem. We are given a graph in which each vertex has an initial and a target color. Each pair of adjacent vertices can swap their current colors. Our goal is to perform the…
In the stable marriage and roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually accepted agents. If any…
We consider the complexity of the recognition problem for two families of combinatorial structures. A graph $G=(V,E)$ is said to be an intersection graph of lines in space if every $v\in V$ can be mapped to a straight line $\ell (v)$ in…
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…
We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can…
This paper is a short introduction to the theory of tangles, both in graphs and general connectivity systems. An emphasis is put on the correspondence between tangles of order k and k-connected components. In particular, we prove that there…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
In the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e.,…
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…
We study the complexity of the Virtual Network Embedding Problem (VNE), which is the combinatorial core of several telecommunication problems related to the implementation of virtualization technologies, such as Network Slicing. VNE is to…