Acta Informatica最新文献

We evaluate the closed forms of the fuzzy topological indices for fuzzy graph structures: the friendship graph and the windmill graph. General expressions are derived for the first and second fuzzy Zagreb indices, the fuzzy Randic index, the fuzzy harmonic index, the fuzzy F-index, the fuzzy Misbalance Prodeg index, the fuzzy Sombor index, and the fuzzy Nirmala index. The formulas are established for arbitrary vertex and edge membership values satisfying the Rosenfeld condition, and therefore apply to a broad class of admissible fuzzy graph structures. Suitable choices of membership values yield explicit closed forms for the fuzzy friendship graph (F_n) and the fuzzy windmill graph (W_{k,n}). The analysis also identifies inconsistencies in previously reported formulas, particularly those arising from incorrect fuzzy degrees, unspecified parameters, and edge memberships that do not agree with the stated graph structures [14]. The practical relevance of the proposed indices is demonstrated through an emergency medical referral network modeled by (F_3) and a renewable-energy microgrid represented by (W_{4,2}), where comparisons between normal and stressed operating conditions reveal changes in connectivity, balance, and system reliability.

The assessment of a job’s Quality of Service (QoS) often revolves around its flow time, also referred to as response time. This study delves into two fundamental objectives for scheduling jobs: the average flow time and the maximum flow time. While the Shortest Remaining Processing Time (SRPT) algorithm minimizes average flow time, it can result in job starvation, causing certain jobs to experience disproportionately long and unfair flow times. In contrast, the First-Come-First-Served (FCFS) algorithm minimizes the maximum flow time but may compromise the average flow time. To strike a balance between these two objectives, a common approach is to minimize the (ell _2) norm of flow time. We first show that SRPT and FCFS are (O(n^{frac{1}{2}}))-competitive for this problem, where n is the number of jobs. Prior to this work, no algorithm was known to achieve a competitive ratio better than SRPT and FCFS. In this paper, we use FCFS to mitigate the starvation caused by SRPT. Given a good estimate of n, we prove that this approach achieves a much better competitive ratio of (O(n^{frac{1}{3}})). To the best of our knowledge, our results provide the first theoretical evidence that mitigating starvation in SRPT leads to a provable improvement in scheduling performance.

The representation number of a graph is the smallest integer k such that the graph can be represented by a word in which each vertex appears exactly k times, and two distinct vertices x and y alternate in the word if and only if they are adjacent in the graph. We extend known results on the representation number for various graph classes to chessboard graphs—namely, king, queen, rook, bishop, and knight graphs. We provide a complete classification for queen graphs and partial classifications or observations for the other classes. As a consequence of our study, we obtain a characterization of all chessboard graphs that are circle graphs. Our work also leads to several interesting open problems.

Vector clock algorithms are fundamental wait-free building blocks that enable the causal ordering of events. As wait-free algorithms, they are designed to complete their operations within a finite number of steps. Stabilizing algorithms aid the system in recovering after the occurrence of transient faults, such as soft errors and arbitrary violations of the assumptions according to which the system was designed to behave. To the best of our knowledge, this paper introduces the first stabilizing vector clock algorithm for asynchronous crash-prone message-passing systems that can achieve wait-free recovery after the occurrence of transient faults. In such settings, demonstrating finite and wait-free recovery from transient faults as well as communication and crash failures, bounding the message and storage sizes, handling the removal of stale information without blocking, and addressing concurrent counter overflow events at different network nodes pose significant challenges. We propose an algorithm that ensures safety in the absence of transient faults and offers bounded time recovery during fair executions following the last transient fault. The novelty lies in guaranteeing a bound on the number of safety violations, even in the absence of execution fairness (where existing algorithms may become permanently blocked due to both transient faults and crash failures). Considering the usefulness of vector clocks in facilitating various elementary synchronization building blocks in asynchronous systems without requiring remote replica synchronization, our analytical insights hold promise for designing other systems that cannot guarantee execution fairness.

We introduce a framework for incremental–decremental maximization that captures the gradual transformation or renewal of infrastructures. In our model, an initial solution is transformed one element at a time and the utility of an intermediate solution is given by the sum of the utilities of the transformed and untransformed parts. We propose a simple randomized algorithm and a more sophisticated deterministic algorithm, both of which find an order in which to transform the elements while maintaining a large utility during all stages of transformation, relative to an optimal solution for the current stage. More specifically, our algorithms yield competitive solutions for utility functions of bounded curvature and/or generic submodularity ratio, and, in particular, for submodular functions and functions satisfying the gross substitutes property. Our results show that incremental–decremental maximization is substantially more difficult than incremental maximization.

In the String Matching in Labeled Graphs (SMLG) problem, we need to determine whether a pattern string appears on a given labeled graph or a given automaton. Under the Orthogonal Vectors hypothesis, the SMLG problem cannot be solved in subquadratic time. In typical bioinformatics applications, pattern matching algorithms should be both fast and space-efficient, so we need to determine useful classes of graphs on which the SLMG problem can be solved efficiently. In this paper, we improve on a recent result that shows how to solve the SMLG problem in linear time on the compressed representation of Wheeler generalized automata, a class of string-labeled automata that extend de Bruijn graphs. More precisely, we show how to remove the assumption that the automata contain no (epsilon)-transitions (namely, edges labeled with the empty string), while retaining the same time and space bounds. This is a significant improvement because (epsilon)-transitions may considerably reduce the size of an automaton recognizing a given language, while capturing the complexity of regular expressions (through Thompson’s construction for converting a regular expression into an equivalent automaton). We prove that, to enable (epsilon)-transitions, we only need to store two additional bitvectors that can be constructed in linear time.

In this paper we focus on the intersection of tile assembling systems, edge-matching puzzles, combinatorial games, and knot construction and identity. As a basis, we utilize the game Celtic!, which is a 2-player board game where the goal of the game is to construct knots where one knot uses more of a player’s pieces than the other player over all knots. All pieces must build off an existing knot and a valid knot must be closed. We consider three variations: a 0-player self-assembly variation that deterministically places pieces to form a closed knot of some length, a 1-player puzzle variation where the goal is to form a closed knot of some length, and the original 2-player game with restricted pieces. We show these are P-complete, NP-complete (depending on the pieces), and PSPACE-complete (for a first-player win), respectively. We nearly fully characterize the hardness of the 1-player puzzle based on the pieces. We prove these results through standard hardness reductions and with constraint logic. Finally, we note some combinatorial game theory strategies to show certain configurations are a draw through strategy stealing.

Let (varGamma ) be a finite additive Abelian group. A subgroup magic rectangle is an (m times n) array (mathbb {S}=(zeta _{i,j})), where (zeta _{i,j} in varGamma ) for all i, j and (|varGamma |=mn), each element appears exactly once in such a way that the set of all row-sums forms a subgroup of order m and the set of all column-sums forms a subgroup of order n. This combinatorial object is a generalisation of the constant sum partition of a finite Abelian group and group magic rectangle. In this article, we discuss the structural properties of subgroup magic rectangles over elementary Abelian 2-groups, Abelian groups whose order is the product of a given prime powers, and provide a characterisation for the existence of a subgroup magic rectangle over (mathbb {Z}_{mn}), where (gcd (m,n)) is odd. Moreover, a recursive backtracking algorithm is given to construct a subgroup magic rectangle over (mathbb {Z}_{mn}).

In medical appointment assignment, unit jobs representing patients arrive online and are assigned to a time slot within their given feasible time interval. We model this setting as interval-constrained online bipartite matching problem. We consider a variant of this problem where reassignments are allowed and extend it by a notion of time that is decoupled from the job arrival events. As jobs arrive, the current point in time gradually advances, and once the time of a slot is passed, the job assigned to it is fixed and cannot be reassigned anymore. We analyze two algorithms for this problem with respect to the resulting matching size and the number of occurring reassignments. We show that FirstFit with reassignments according to the shortest augmenting path rule is exactly (frac{2}{3})-competitive with respect to the matching cardinality. The competitive ratio remains (frac{2}{3}) if we restrict FirstFit to consider only augmenting paths causing at most a constant number of reassignments, which implies a linear number of reassignments in total. This fills the gap between the known optimal algorithm with no reassignments at all, which is (frac{1}{2})-competitive, on the one hand, and an earliest-deadline-first strategy (EDF), which we prove to be 1-competitive in our over-time framework, but which suffers (Omega (n^2)) reassignments in the worst case, on the other. We further extend the problem setting to the sets of feasible slots per job that are not intervals. In this setting, FirstFit remains (frac{2}{3})-competitive, which is optimal with respect to the matching cardinality, while EDF loses its optimality.

We consider a game-theoretic variant of maximizing a monotone increasing, submodular function under a cardinality constraint. Initially, a solution to this classic problem is determined. Subsequently, a predetermined number of elements from the ground set, not necessarily contained in the initial solution, are deleted, potentially reducing the solution’s cardinality. If any deleted elements were part of the initial solution, they are replaced with a set of at most equal cardinality. The objective is to maximize the value of the ultimate solution, with the deletion being maximally disadvantageous to the ultimate solution. When the submodular function is ({{,mathrm{ text {M}^natural },}})-concave, we prove that a simple greedy algorithm computes an optimal solution. When only one element may be deleted, we propose a polynomial running time algorithm with an approximation factor of at least (frac{1}{3}). When the number of deletions may become as large as the cardinality parameter, we present a polynomial running time algorithm that approximates an optimal ultimate solution in dependence on the curvature of the submodular function. Furthermore, assuming that the number of allowed deletions is upper bounded by a term of the order of (frac{k}{log _2^2(k)}), where k is the cardinality parameter, we adapt an algorithm from Bogunovic et al. and show that its approximation factor is at least 0.108.