Information Processing Letters最新文献

We study open swarms and teams of multi-agent systems where agents may join or leave the system at runtime. Kouvaros et al. [1] defined the verification problem for such systems and showed it to be undecidable, in general. Also, they have found one decidable class of open multi-agent systems and provided a partial decision procedure for another. In the same vein we present a subclass of open teams called regular open teams for which reachability is decidable. This is shown by employing a counter abstraction technique wherein the regular open team is abstracted into a finite state multi-counter system.

In minimum power network design problems we are given an undirected graph $G=(V,E)$ with edge costs $\{c_e:e\in E\}$. The goal is to find an edge set $F\subseteq E$ that satisfies a prescribed property of minimum power $p_c\left(F\right)={\sum }_{v\in V}\max \{c_e:e\in F\text{ is incident to }v\}$. In the Min-Power k Edge Disjoint st-Paths problem F should contain k edge disjoint st-paths. The problem admits a k-approximation algorithm, and it was an open question to achieve an approximation ratio sublinear in k for simple graphs, even for unit costs. We give a $2\sqrt{2k}$-approximation algorithm for general costs.

We reconsider two well-known distributed randomized algorithms computing a maximal independent set, proposed in the seminal work of Luby (1986). We enhance these algorithms such that they become self-stabilizing without sacrificing their run-time, i.e., both stabilize in $O(\log n)$ synchronous rounds with high probability on any n-node graph. The first algorithm gets along with three states, but needs to know an upper bound on the maximum degree. The second does not need any information about the graph, but uses a number of states that is linear in the node degree. Both algorithms use messages of logarithmic size.

For a class $G$ of graphs, the objective of Subgraph Complementation to $G$ is to find whether there exists a subset S of vertices of the input graph G such that modifying G by complementing the subgraph induced by S results in a graph in $G$. We obtain a polynomial-time algorithm for the problem when $G$ is the class of graphs with minimum degree at least k, for a constant k, answering an open problem by Fomin et al. (Algorithmica, 2020). When $G$ is the class of graphs without any induced copies of the star graph on $t+1$ vertices (for any constant $t\ge 3$) and diamond, we obtain a polynomial-time algorithm for the problem. This is in contrast with a result by Antony et al. (Algorithmica, 2022) that the problem is NP-complete and cannot be solved in subexponential-time (assuming the Exponential Time Hypothesis) when $G$ is the class of graphs without any induced copies of the star graph on $t+1$ vertices, for every constant $t\ge 5$.

The problem that we consider is the following: given an $n\times n$ array A of positive numbers and a natural number p, find a tiling using at most p rectangles (which means that each array element must be covered by some rectangle and no two rectangles must overlap) that minimizes the maximum weight of any rectangle (the weight of a rectangle is the sum of elements which are covered by it). We prove that it is NP-hard to approximate this problem to within a factor of 1$\frac{1}{3}$ (the previous best result was $1\frac{1}{4}$).

We robustify PCTL and PCTL^⁎, the most important specification languages for probabilistic systems, and show that robustness does not increase the complexity of their model-checking problems.

A subset S of the vertex set of a graph G is an $F$-isolating set of G if $G-N\left[S\right]$ does not contain a copy of a member of $F$ as a subgraph, where $F$ is a family of connected graphs and $N\left[S\right]$ is the closed neighborhood of S. The $F$-isolation number of G is the minimum cardinality of an $F$-isolating set of G, denoted by $\iota (G,F)$. Given a graph G, $\left\{P_k\right\}$-ISOLATION asks for the size of a smallest $\left\{P_k\right\}$-isolating set of G for a fixed positive integer k, where $P_k$ is a path of order k. In this paper, we first show that the decision version of $\left\{P_k\right\}$-ISOLATION is NP-complete for chordal graphs and planar graphs. Secondly, we propose a linear time algorithm to compute a smallest $\left\{P_k\right\}$-isolating set of a tree. Finally, we solve the problem of characterizing the connected graphs G with $\iota (G,\{P_3\left\}\right)=\frac{2}{7}\left|V\right(G\left)\right|$, proposed by Zhang and Wu [Discrete Appl. Math. 304 (2021) 365-374].

Using the notion of visibility representations, our paper establishes a new property of instances of the Nondeterministic Constraint Logic (NCL) problem (a PSPACE-complete problem that is very convenient to prove the PSPACE-hardness of reversible games with pushing blocks). Direct use of this property introduces an explosion in the number of gadgets needed to show PSPACE-hardness, but we show how to bring that number from 32 down to only three in the general case, and down to two in our specific case! We propose it as a step towards a broader and more general framework for studying games with irreversible gravity, and use this connection to guide an indirect polynomial-time many-one reduction from the NCL problem to the Hanano Puzzle—which is NP-hard—to prove it is PSPACE-complete.

Fair division is a longstanding problem in economics and has recently received substantial interest in computer science. Several applications of fair division involve agents with unequal entitlements represented by weights. We review work on weighted fair division of indivisible items, discuss the range of weighted fairness notions that have been proposed, and highlight a number of open questions.