Information Processing Letters最新文献

Recently we established an analog of Gabbay's separation theorem about linear temporal logic (LTL) for the extension of Moszkowski's discrete time propositional Interval Temporal Logic (ITL) by two sets of expanding modalities, namely the unary neighbourhood modalities and the binary weak inverses of ITL's chop operator. One of the many useful applications of separation in LTL is the concise proof of LTL's expressive completeness wrt the monadic first-order theory of $〈\omega ,<〉$ it enables. In this paper we show how our separation theorem about ITL facilitates a similar proof of the expressive completeness of ITL with expanding modalities wrt the monadic first- and second-order theories of $〈Z,<〉$.

We study a robust single-machine scheduling problem with uncertain processing times on a serial-batch processing machine to minimize maximum lateness. The problem can model many practical production and logistics applications which involve uncertain factors such as defect rates. A solution to a batch scheduling problem can be represented as a combination of a job-processing sequence and a partition of this sequence (batch sizing). To solve the problem, we prove that the job ordering rule for the earliest due date is optimal for any uncertainty set. For the batch sizing problem, we propose an exact algorithm based on dynamic programming with the same time complexity as solving the nominal problem.

Glaßer et al. (SIAMJCOMP 2009 and TCS 2009) proved that NP-complete languages are polynomial-time mitotic for the many-one reduction, meaning that each NP-complete language L can be split into two NP-complete languages $L\cap S$ and $L\cap \bar{S}$, where S is a language in P. It follows that every NP-complete language can be partitioned into an arbitrary finite number of NP-complete languages. We strengthen and generalize this result by showing that every NP-complete language can be partitioned into infinitely many NP-complete languages. Furthermore those NP-complete languages resulting from such partitioning can be effectively presented.

We study the α-Fixed Cardinality Graph Partitioning (α-FCGP) problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph G, two numbers $k,p$ and $0\le \alpha \le 1$, the question is whether there is a set $S\subseteq V$ of size k with a specified coverage function ${\mathrm{cov}}_{\alpha }\left(S\right)$ at least p (or at most p for the minimization version). The coverage function ${\mathrm{cov}}_{\alpha }(\cdot )$ counts edges with exactly one endpoint in S with weight α and edges with both endpoints in S with weight $1-\alpha$. α-FCGP generalizes a number of fundamental graph problems such as Densest k-Subgraph, Max k-Vertex Cover, and Max $(k,n-k)$-Cut.

A natural question in the study of α-FCGP is whether the algorithmic results known for its special cases, like Max k-Vertex Cover, could be extended to more general settings. One of the simple but powerful methods for obtaining parameterized approximation [Manurangsi, SOSA 2019] and subexponential algorithms [Fomin et al. IPL 2011] for Max k-Vertex Cover is based on the greedy vertex degree orderings. The main insight of our work is that the idea of greedy vertex degree ordering could be used to design fixed-parameter approximation schemes (FPT-AS) for $\alpha >0$ and subexponential-time algorithms for the problem on apex-minor free graphs for maximization with $\alpha >1/3$ and minimization with $\alpha <1/3$.⁴

This paper considers the problem of exploring an unknown rectangular cellular environment with a rectangular hole using a mobile robot. The robot's task is to visit each cell at least once and return to the start. The robot has limited visibility that can only detect four cells adjacent to it. And it has large amount of memory that can store a map of discovered cells. The goal of this work is to find the shortest exploration tour, that is, minimizing the total number of multiple visited cells. We consider the environment in four possible scenarios: rectangular, L-shaped, C-shaped or O-shaped grid polygon. An on-line strategy has been proposed for these scenarios. We prove that it is optimal for rectangular, L-shaped, C-shaped grid polygon, and is 4/3-competitive for O-shaped grid polygon.

Enumeration problems are often encountered as key subroutines in the exact computation of graph parameters such as chromatic number, treewidth, or treedepth. In the case of treedepth computation, the enumeration of inclusion-wise minimal separators plays a crucial role. However and quite surprisingly, the complexity status of this problem has not been settled since it has been posed as an open direction by Kloks and Kratsch in 1998. Recently at the PACE 2020 competition dedicated to treedepth computation, solvers have been circumventing that by listing all minimal a-b separators and filtering out those that are not inclusion-wise minimal, at the cost of efficiency. Naturally, having an efficient algorithm for listing inclusion-wise minimal separators would drastically improve such practical algorithms. In this note, however, we show that no efficient algorithm is to be expected from an output-sensitive perspective, namely, we prove that there is no output-polynomial time algorithm for inclusion-wise minimal separators enumeration unless $P=\mathrm{NP}$.

We present an innovative approach for capturing the complexity of ω-regular languages using the concept of flowers. This semantic tool combines two syntax-based definitions, namely the Mostowski hierarchy of word languages and syntactic flowers. The former is based on deterministic parity automata with a limited number of priorities, while the latter simplifies deterministic parity automata by reducing the number of priorities used, without altering their structure. Synthesising these two approaches yields a semantic concept of flowers, which offers a more effective way of dealing with the complexity of ω-regular languages. This letter provides a comprehensive definition of semantic flowers and shows that it captures the complexity of ω-regular languages. We also show that this natural concept yields simple proofs of the expressive power of good-for-games automata.