Theoretical Computer Science最新文献

Reducing traffic congestion and increasing passenger safety are important objectives for emerging automated transportation systems. Autonomous intersection management systems (AIMS) enable large scale optimization of vehicle trajectories with connected and autonomous vehicles (CAVs). We propose a novel approach for computing the fastest waypoint trajectory in intersections using graph search in a discretized space-time graph that produces collision-free paths with variable vehicle speeds that comply with traffic rules and vehicle dynamical constraints. To assist our planner algorithm in decentralized scenarios, we also propose a multi-agent protocol architecture for vehicle coordination for trajectory planning using a vehicle-to-vehicle (V2V) network. The trajectories generated allow a much higher evacuation rate and congestion threshold, with lower $O\left(N\right)$ algorithm runtime compared to the state of the art conflict detection graph platoon path planning method, even for large scenarios with vehicle arrival rate of $1/s$ and thousands of vehicles.

The reconstruction of a (hyper)graph starting from its degree sequence is one of the most relevant among the inverse problems investigated in the field of graph theory. In case of graphs, a feasible solution can be quickly reached, while in case of hypergraphs Deza et al. (2018) proved that the problem is NP-hard even in the simple case of 3-uniform ones. This result opened a new research line consisting in the detection of instances for which a solution can be computed in polynomial time. In this work we deal with 3-uniform hypergraphs, and we study them from a different perspective, exploiting a connection of these objects with partially ordered sets. More precisely, we introduce a simple partially ordered set, whose ideals are in bijection with a subclass of 3-uniform hypergraphs. We completely characterize their degree sequences in case of principal ideals (here a simple fast reconstruction strategy follows), and we furthermore carry on a complete analysis of those degree sequences related to the ideals with two generators. We also consider unique hypergraphs in $D^{ext}$, i.e., those hypergraphs that do not share their degree sequence with other non-isomorphic ones. We show that uniqueness holds in case of hypergraphs associated to principal ideals, and we provide some examples of hypergraphs in $D^{ext}$ where this property is lost.

Constructions of Boolean functions with various cryptographic properties have always been an important challenge in cryptography. This paper proposes systematic constructions of even-variable rotation symmetric Boolean functions satisfying almost all cryptographic criteria, that is, resiliency, optimal algebraic degree, strict avalanche criterion, high nonlinearity, nonexistence of nonzero linear structures, good global avalanche characteristics. Moreover, some of the constructions also have high algebraic immunity. This is the first time that Boolean functions having such cryptographic properties are obtained, which can be considered as good candidates for the design of real-life encryption schemes.

The deterministic k-server conjecture states that there is a k-competitive deterministic algorithm for the k-server problem for any metric space. We show that the work function algorithm is 3-competitive for the 3-server problem on circle metrics, a case left open by Coester and Koutsoupias (2021). Our analysis follows the existing framework but introduces a new potential function which may be viewed as a relaxation of the counterpart by Coester and Koutsoupias (2021). We further notice that the new potential function and many existing ones can be rewritten in a canonical form. Through a computer-aided verification, however, we find that no such canonical potential function can resolve the deterministic 3-server conjecture for general metric spaces under the current analysis framework.

The Steiner Multicycle problem consists in, given a complete graph, a weight function on its edges, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint cycles in the graph such that, for every terminal set, all of its vertices are in a same cycle of the collection. This problem generalizes the Traveling Salesman problem and, therefore, is hard to approximate in general. On the practical side, it models a collaborative less-than-truckload problem with pickup and delivery locations. Using an algorithm for the Survivable Network Design problem and T-joins, we obtain a 3-approximation for the metric case, improving on the previous best 4-approximation. Furthermore, we present an (11/9)-approximation for the particular case of the Steiner Multicycle in which each edge weight is 1 or 2. This algorithm can be adapted to obtain a (7/6)-approximation when every terminal set contains at least four vertices. Finally, we devise an $O(\lg n)$-approximation algorithm for the asymmetric version of the problem.

As high performance computing systems consisting of multiple processors play an important role in big data analytics, we are motivated to focus on the research of reliability, design-for-test, fault diagnosis and detection of large-scale multiprocessor interconnected systems. System-level diagnosis theory, which originates from the testing of VLSI and Wafer, aims to identify faulty processors in these systems by means of analyzing the test results among the processors, while diagnosability as well as diagnosis accuracy are two important indices. The probabilistic fault diagnostic strategy seeks to correctly diagnose processors with high probability under the assumption that each processor has a certain failing probability. In this work, based on the probabilistic diagnosis algorithm with consideration of fault clustering, we specialize in the local diagnostic capability to establish the probability that any processor in a discrete status is diagnosed correctly. Subsequently, we investigate the global performance evaluation of multiprocessor systems under various significant fault distributions including Poisson distribution, Exponential distribution and Binomial distribution. In addition, we directly apply our results to the data center network $HSDC$ and $(n,k)$-star network. Numerical simulations are performed to verify the established results, which reveal the relationship between the accuracy of correct diagnosis and regulatory parameters.

Symbolic heaps, which are a restricted class of separation logic formulas, with inductive definitions are a suitable language in automated verification systems for memory-manipulating programs. In this context, some related problems, e.g., the entailment problem, have been studied theoretically. In addition, several solvers for the entailment problem based on the proof-search algorithm in cyclic-proof systems, which are proof systems in sequent calculus style with cyclic structure, have been proposed. However, the cut-elimination property generally does not hold for cyclic-proof systems of symbolic heaps with inductive definitions, which means that searching for a cut-free proof is insufficient. In other words, we hope to find a reasonable proof-search algorithm considering the cut rule or we give up on obtaining a complete proof-search procedure. This paper investigates this issue and demonstrates a limit to the challenge of the restrictions on the cut rule in a cyclic-proof system for symbolic heaps. We propose a restricted cut rule, referred to as the presumable cut, which is a relaxed variant of the analytic cut, in which the cut formula must be a subformula of the bottom sequent. This paper demonstrates that the provability of the cyclic-proof system for symbolic heaps becomes strictly weaker by restricting the cut rule to the presumable cut.

We consider the problem of sampling elements with some desired property from a large set, without testing the property of interest, but with the (probabilistic) assurance to have at least one match among the random sample. Like in ranked set sampling (RSS), we consider an infinite population under study, whose properties of interest are too expensive and/or time-consuming to measure. Unlike RSS, we are void of a ranking mechanism, so our sampling is done entirely blind. We show how it is nonetheless doable to assure, with controllably large likelihood, to either have at least one of the interesting elements in a random sample, or, contrarily, sample with the likewise assurance of not having one of the interesting elements in the sample. Our technique utilizes density bounds for distributions and threshold functions from random graph theory.