Related papers: Forbidden lists (NP and CSP for combinatorialists)
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
In this Part II, we apply the general theory developed in Part I to a detailed analysis of the Constraint Satisfaction Problem (CSP). We show how specific types of resolution rules can be defined. In particular, we introduce the general…
Computational intractability has for decades motivated the development of a plethora of methodologies that mainly aimed at a quality-time trade-off. The use of Machine Learning techniques has finally emerged as one of the possible tools to…
In recent work by Johnson et al. (2022), a framework was described for the study of graph problems over classes specified by omitting each of a finite set of graphs as subgraphs. If a problem falls into the framework then its computational…
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…
We strengthen a result by Laskar and Lyle (Discrete Appl. Math. (2009), 330-338) by proving that it is NP-complete to decide whether a bipartite planar graph can be partitioned into three independent dominating sets. In contrast, we show…
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full…
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…
We introduce the Multicolored Graph Realization problem (MGRP). The input to the problem is a colored graph $(G,\varphi)$, i.e., a graph together with a coloring on its vertices. We can associate to each colored graph a cluster graph…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms…
We elaborate upon the formal foundations of hybrid Answer Set Programming (ASP) and extend its underlying logical framework with aggregate functions over constraint values and variables. This is achieved by introducing the construct of…
We consider the problem of combining machine learning models to perform higher-level cognitive tasks with clear specifications. We propose the novel problem of Visual Discrimination Puzzles (VDP) that requires finding interpretable…
In this paper, we consider the maximum $k$-edge-colorable subgraph problem. In this problem we are given a graph $G$ and a positive integer $k$, the goal is to take $k$ matchings of $G$ such that their union contains maximum number of…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…
For bipartite graphs the NP-completeness is proved for the problem of existence of maximum matching which removal leads to a graph with given lower(upper)bound for the cardinality of its maximum matching.
The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…