Journal of Computer and System Sciences最新文献

We introduce the problem of adapting a stable matching to forced and forbidden pairs. Given a stable matching $M_1$, a set Q of forced pairs, and a set P of forbidden pairs, we want to find a stable matching that includes all pairs from Q, no pair from P, and is as close as possible to $M_1$. We study this problem in four classic stable matching settings: Stable Roommates (with Ties) and Stable Marriage (with Ties). Our main contribution is a polynomial-time algorithm, based on the theory of rotations, for adapting Stable Roommates matchings to forced pairs. In contrast, we show that the same problem for forbidden pairs is NP-hard. However, our polynomial-time algorithm for forced pairs can be extended to a fixed-parameter tractable algorithm with respect to the number of forbidden pairs. Moreover, we study the setting where preferences contain ties: Some of our algorithmic results can be extended while other problems become intractable.

The radio k-chromatic number $r{c}_k\left(G\right)$ of a graph G is the minimum integer λ such that there exists a function $\varphi :V\left(G\right)\to \{0,1,\cdots ,\lambda \}$ satisfying $\left|\varphi \right(u)-\varphi (v\left)\right|\ge k+1-d(u,v)$, where $d(u,v)$ denotes the distance between u and v. A considerable amount of attention has been given to find the exact values or providing polynomial time algorithms to determine $r{c}_k\left(G\right)$ for several basic graph families such as paths, cycles, trees, and powers of paths, usually for some specific values of k. In this article, we find the exact values of $r{c}_k\left(G\right)$ where G is a power of a path with diameter strictly less than k. Our proof readily provides a linear time algorithm for assigning a radio k-coloring of G. Furthermore, our proof technique is a potential tool for solving the same problem for other classes of graphs having “small” diameters.

Token Sliding Optimization asks whether there exists a sequence of at most ℓ steps that transforms independent set S into T, where at each step a token slides to an unoccupied neighboring vertex (while maintaining independence). In Token Jumping Optimization, we are instead allowed to jump from a vertex to any unoccupied vertex. Both problems are known to be FPT when parameterized by ℓ on nowhere dense graphs. In this work, we show that both problems are FPT for parameter $k+\ell +d$ on d-degenerate graphs as well as for parameter $\left|M\right|+\ell +\Delta$ on graphs having a modulator M to maximum degree Δ. We complement these results by showing that for parameter ℓ both problems become hard already on 2-degenerate graphs. Finally, we show that using such families one can obtain a unified algorithm for the standard Token Jumping problem parameterized by k on degenerate and nowhere dense graphs.

We study the problem of reconfiguring s-t-separators on finite simple graphs. We consider several variants of the problem, focusing on the token sliding and jumping models. We begin with a polynomial-time algorithm that computes (if one exists) a shortest sequence of slides and another that decides if a sequence of jumps exists and outputs a witnessing sequence. We also show that deciding if a reconfiguration sequence of at most ℓ jumps exists is an $\text{NP}$-complete problem. To complement this result, we investigate the parameterized complexity of the natural parameterizations of the problem: by the size k of the minimum s-t-separators and by the number of jumps ℓ. We show that the problem is in FPT parameterized by k, but that it does not admit a polynomial kernel unless $\text{NP}\subseteq \text{coNP/poly}$. Our final result is a kernel with $O\left({\ell }^2\right)$ vertices and edges.

In real life, data are often of poor quality as a result, for instance, of uncertainty, mismeasurements, missing values or bad inputs. This issue hampers an implicit yet crucial operation of every database management system: equality testing. Indeed, equality is, in the end, a context-dependent operation with a plethora of interpretations. In practice, the treatment of different types of equality is left to programmers, who have to struggle with those interpretations in their code. We introduce a lattice-based declarative framework to address this problem. It allows specification of numerous semantics for equality at a high level of abstraction. To go beyond tuple equality, we study functional dependencies (FDs) in the light of our framework. First, we define abstract FDs, generalizing classical FDs. These lead to the consideration of particular interpretations of equality: realities. Building upon realities and possible/certain answers, we introduce possible/certain FDs and give some complexity results.

We study the complexity of reasoning tasks for logics in team semantics. Our main focus is on the data complexity of model checking but we also derive new results for logically defined counting and enumeration problems. Our approach is based on modular reductions of these problems into the corresponding problems of various classes of Boolean formulas. We illustrate our approach via several new tractability/intractability results.

A graph is temporally connected if a strict temporal path exists from every vertex u to every other vertex v. This paper studies temporal design problems for undirected temporally connected graphs. Given a connected undirected graph G, the goal is to determine the smallest total number of time-labels $\left|\lambda \right|$ needed to ensure temporal connectivity, where $\left|\lambda \right|$ denotes the sum, over all edges, of the size of the set of labels associated to an edge. The basic problem, called Minimum Labeling (ML) can be solved optimally in polynomial time. We introduce the Min. Aged Labeling (MAL) problem, which involves connecting the graph with an upper-bound on the maximum label, the Min. Steiner Labeling (MSL) problem, focusing on connecting specific important vertices, and the age-restricted version of MSL, Min. Aged Steiner Labeling (MASL). We show that MAL is NP-complete, MASL is W[1]-hard, and while MSL remains NP-hard, it is FPT with respect to the number of terminals.

Dietze's conjecture concerns the problem of equipping a tree automaton M with weights to make it probabilistic, in such a way that the resulting automaton N predicts a given corpus $C$ as accurately as possible. The conjecture states that the accuracy cannot increase if the states in M are merged with respect to an equivalence relation ∼ so that the result is a smaller automaton $M^{\sim }$. Put differently, merging states can never improve predictions. This is under the assumption that both M and $M^{\sim }$ are bottom-up deterministic and accept every tree in $C$. We prove that the conjecture holds, using a construction that turns any probabilistic version $N^{\sim }$ of $M^{\sim }$ into a probabilistic version N of M, such that N assigns at least as great a weight to each tree in $C$ as $N^{\sim }$ does.

Connectivity is one of important parameters for the fault tolerant of an interconnection network. In 1996, Fàbrega and Fiol proposed the concept of g-extra connectivity. A subset of vertices S is said to be a cutset if $G-S$ is not connected. A cutset S is called an $R_g$-cutset, where g is a non-negative integer, if every component of $G-S$ has at least $g+1$ vertices. If G has at least one $R_g$-cutset, the g-extra connectivity of G, denoted by ${\kappa }_g\left(G\right)$, is then defined as the minimum cardinality over all $R_g$-cutsets of G. In this paper, we first obtain the exact value of g-extra connectivity for the lexicographic product of two general graphs. Next, the upper and lower sharp bounds of g-extra connectivity for the Cartesian product of two general graphs are given. In the end, we apply our results on grid graphs and 2-dimensional generalized hypercubes.