Related papers: Improved Algorithms for 3-Coloring, 3-Edge-Colorin…
We show how the implementation of conservative logic gates on flow networks suggests a way to solve 3SAT and 3-dimensional matching problems in polynomial time by using standard minimum-cost flow methods.
We continue the investigation of polynomial-time sparsification for NP-complete Boolean Constraint Satisfaction Problems (CSPs). The goal in sparsification is to reduce the number of constraints in a problem instance without changing the…
For any odd $t\ge 9$, we present a polynomial-time algorithm that solves the $3$-colouring problem, and finds a $3$-colouring if one exists, in $P_{t}$-free graphs of odd girth at least $t-2$. In particular, our algorithm works for $(P_9,…
In this paper, we introduce a methodology, called decomposition-based reductions, for showing the equivalence among various problems of bounded-width. First, we show that the following are equivalent for any $\alpha > 0$: * SAT can be…
This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…
We model Semantic Self-Verification (SSV) as the problem of determining whether a statement accurately characterizes its own semantic properties within a given interpretive framework that formalizes a challenge in AI safety and fairness:…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
The question of whether 3-Coloring can be solved in polynomial-time for the diameter two graphs is a well-known open problem in the area of algorithmic graph theory. We study the problem restricted to graph classes that avoid cycles of…
Constraint Satisfaction Problems (CSPs) present significant challenges to artificial intelligence due to their intricate constraints and the necessity for precise solutions. Existing symbolic solvers are often slow, and prior research has…
There is no known polynomial-time algorithm that can solve an NP problem. Evolutionary search has been shown to be a viable method of finding acceptable solutions within a reasonable time period. Recently quantum computers have surfaced as…
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…
We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in…
The article studies edge coverage for control flow graphs extended with explicit constraints. Achieving a given level of white-box coverage for a given code is a classic problem in software testing. We focus on designing test sets that…
This paper sets out the results of a range of searches for linear and cyclic graph colourings with specific Ramsey properties. The new graphs comprise mainly 'template graphs' which can be used in a construction described by the current…
We build on a recently proposed method for stepwise explaining solutions of Constraint Satisfaction Problems (CSP) in a human-understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified…
Many practitioners who use the EM algorithm complain that it is sometimes slow. When does this happen, and what can be done about it? In this paper, we study the general class of bound optimization algorithms - including…
Maximum Clique Problem(MCP) is one of the 21 original NP--complete problems enumerated by Karp in 1972. In recent years a large number of exact methods to solve MCP have been appeared(Babel, Wood, Kumlander, Fahle, Li, Tomita and etc). Most…
The constrained synchronization problem (CSP) asks for a synchronizing word of a given input automaton contained in a regular set of constraints. It could be viewed as a special case of synchronization of a discrete event system under…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…