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Dejan Delic

Publications and source records attributed to Dejan Delic.

6 recordsLinked to original sources
arXiv2025

The Constraint Satisfaction Problem Over Multisorted Cores

Constraint Satisfaction Problems (CSPs, for short) make up a class of problems with applications in many areas of computer science. The first classification of these problems was given by Schaeffer who showed that every CSP over the domain {0,1} is either in P or is NP-complete. More recently this was shown to hold for all CSPs over finite relational structures independently by Bulatov and Zhuk. Furthermore, they characterized the complexity based solely on the polymorphism algebra of the associated relational structure, building upon the deep connections between universal algebra and complexity theory. In this article we extend this and consider what happens if the instance forms a special type of relational core called a multisorted core. Our main result is that in this case the problem is reducible to computing the determinant of an integer valued matrix which places it in the complexity class DET, which is likely a strict subset of P.

cs.CC↗
arXiv2015

A finer reduction of constraint problems to digraphs

It is well known that the constraint satisfaction problem over a general relational structure A is polynomial time equivalent to the constraint problem over some associated digraph. We present a variant of this construction and show that the corresponding constraint satisfaction problem is logspace equivalent to that over A. Moreover, we show that almost all of the commonly encountered polymorphism properties are held equivalently on the A and the constructed digraph. As a consequence, the Algebraic CSP dichotomy conjecture as well as the conjectures characterizing CSPs solvable in logspace and in nondeterministic logspace are equivalent to their restriction to digraphs.

cs.CC↗
arXiv2013

Distinguishing homomorphisms of infinite graphs

We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph $G$ satisfies the connected existentially closed property and admits a homomorphism to $H$, then it admits continuum-many distinguishing homomorphisms from $G$ to $H$ join $K_2.$ Applications are given to a family universal $H$-colourable graphs, for $H$ a finite core.

math.CO↗
arXiv2013

On the reduction of the CSP dichotomy conjecture to digraphs

It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the algebraic dichotomy conjecture is equivalent to its restriction to digraphs and that the polynomial reduction can be made in logspace. We also show that our reduction preserves the bounded width property, i.e., solvability by local consistency methods. We discuss further algorithmic properties that are preserved and related open problems.

cs.CC↗