Related papers: Efficient enumeration of solutions produced by clo…
In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure of a boolean relation (a set of boolean vectors) by…
The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of…
We consider a set system $(V, {\mathcal C}\subseteq 2^V)$ on a finite set $V$ of elements, where we call a set $C\in {\mathcal C}$ a component. We assume that two oracles $\mathrm{L}_1$ and $\mathrm{L}_2$ are available, where given two…
We study the problem of generating monomials of a polynomial in the context of enumeration complexity. In this setting, the complexity measure is the delay between two solutions and the total time. We present two new algorithms for…
Given an implicational base, a well-known representation for a closure system, an inconsistency binary relation over a finite set, we are interested in the problem of enumerating all maximal consistent closed sets (denoted by MCCEnum for…
When a problem has more than one solution, it is often important, depending on the underlying context, to enumerate (i.e., to list) them all. Even when the enumeration can be done in polynomial delay, that is, spending no more than…
Dependence logics are a modern family of logics of independence and dependence which mimic notions of database theory. In this paper, we aim to initiate the study of enumeration complexity in the field of dependence logics and thereby get a…
In this paper, as a new notion, we define a transitive system to be a set system $(V, {\mathcal C}\subseteq 2^V)$ on a finite set $V$ of elements such that every three sets $X,Y,Z\in{\mathcal C}$ with $Z\subseteq X\cap Y$ implies $X\cup…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
In this paper independent sets of closure operations are introduced. We characterize minimal keys and antikeys of closure operations in terms of independent sets. We establish an expression on the connection between minimal keys and…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
The quality of enumeration algorithms is often measured by their delay, that is, the maximal time spent between the output of two distinct solutions. If the goal is to enumerate $t$ distinct solutions for any given $t$, then another…
We investigate the relationship between several enumeration complexity classes and focus in particular on problems having enumeration algorithms with incremental and polynomial delay (IncP and DelayP respectively). We show that, for some…
Enumerating the result set of a first-order query over a relational structure of bounded degree can be done with linear preprocessing and constant delay. In this work, we extend this result towards the compressed perspective where the…
New and old results on closed polynomials, i.e., such polynomials f in K[x_1,...,x_n] that the subalgebra K[f] is integrally closed in K[x_1,...,x_n], are collected. Using some properties of closed polynomials we prove the following…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
We present in this paper a new procedure to saturate a set of clauses with respect to a well-founded ordering on ground atoms such that A < B implies Var(A) {\subseteq} Var(B) for every atoms A and B. This condition is satisfied by any atom…
We define the parametric closure problem, in which the input is a partially ordered set whose elements have linearly varying weights and the goal is to compute the sequence of minimum-weight lower sets of the partial order as the weights…
The classes Delay-FPT and Total-FPT recently have been introduced into parameterized complexity in order to capture the notion of efficiently solvable parameterized enumeration problems. In this paper we focus on ordered enumeration and…