A minimal siphon (or alternatively a structural deadlock) of a Petri net is defined as a minimal set S of places such that existence of any edge from a transition t to a place of S implies that there is an edge from s...
详细信息
A minimal siphon (or alternatively a structural deadlock) of a Petri net is defined as a minimal set S of places such that existence of any edge from a transition t to a place of S implies that there is an edge from some place of S to t. The subject of the paper is to find a minimal siphon containing a given set of specified places of a general Petri net.
The complexity of graph isomorphism (GRAPHISO) is a famous problem in computer science. For graphs G and H, it asks whether they are the same up to a relabeling of vertices. In 1981, Lubiw proved that list restricted ...
详细信息
The complexity of graph isomorphism (GRAPHISO) is a famous problem in computer science. For graphs G and H, it asks whether they are the same up to a relabeling of vertices. In 1981, Lubiw proved that list restricted graph isomorphism (LISTISO) is NP-complete: for each u is an element of V(G), we are given a list L(u) subset of V(H) of possible images of u. After 35 years, we revive the study of this problem and consider which results for GraphIso can be modified to solve ListIso. We prove: 1) Under certain conditions, GI-completeness of a class of graphs implies NP-completeness of ListIso. 2) Several combinatorial algorithms for GraphIso can be modified to solve ListIso: for trees, planar graphs, interval graphs, circle graphs, permutation graphs, and bounded treewidth graphs. 3) ListIso is NP-complete for cubic colored graphs with sizes of color classes bounded by 8 with all lists of size at most 3. (C) 2021 The Author(s). Published by Elsevier B.V.
We study a multiechelon lot-sizing problem for a serial supply chain that consists of a production level and several transportation levels, where the demands can exist in the production echelon as well as in any trans...
详细信息
We study a multiechelon lot-sizing problem for a serial supply chain that consists of a production level and several transportation levels, where the demands can exist in the production echelon as well as in any transportation echelons. With the presence of stationary production capacity and general cost functions, our model integrates production, inventory, and transportation decisions and generalizes existing literature on many multiechelon lot-sizing models. First, we answer an open question in the literature by showing that multiechelon lot sizing with intermediate demands (MIS) is NP-hard. Second, we develop polynomialtimealgorithms for both uncapacitated and capacitated MIS with a fixed number of echelons. The run times of our algorithms improve on those of many known algorithms for different MIS models. Third, we present families of valid inequalities for MIS that generalize known inequalities. For the uncapacitated case, we develop a polynomial-time separation algorithm and efficient separation heuristics. Finally, we demonstrate the effectiveness of a branch-and-cut algorithm using proposed inequalities to solve large multi-item MIS problems.
We consider single-hop wavelength-division multiplexed networks in which the transmitters take a nonzero amount of time, called tuning latency, to tune from one wavelength to another. For such networks, we show that, ...
详细信息
We consider single-hop wavelength-division multiplexed networks in which the transmitters take a nonzero amount of time, called tuning latency, to tune from one wavelength to another. For such networks, we show that, under certain conditions on the traffic matrix, there exist polynomial-time algorithms that produce the optimal schedule. Further, the tuning latency is masked in the length of the optimal schedule. Using Chernoff-Hoeffding bounds, we show that the condition on the traffic matrix is satisfied with high probability when the wavelength reuse factor is large, i.e., the number of nodes is large compared to the number of wavelengths. Simulation results show the dramatic improvement in the performance of the network using our algorithm as compared with other heuristics.
Let (G, c, w) be an edge-colored weighted graph, where G is a nontrivial connected graph, c is an edge-coloring of G, and w is an edge-weighting of G. A path, a trail, a cycle, or a closed trail of G, say F, is called...
详细信息
Let (G, c, w) be an edge-colored weighted graph, where G is a nontrivial connected graph, c is an edge-coloring of G, and w is an edge-weighting of G. A path, a trail, a cycle, or a closed trail of G, say F, is called proper under the edge-coloring c if every two consecutive edges of F receive different colors in c. Let s and t be two specified nonadjacent vertices in G. In this paper, we study the problems for finding, in (G, c, w), the minimum weighted proper s-t-path, the minimum weighted proper s-t-trail, the minimum weighted proper cycle, the minimum weighted proper closed trail, the maximum weighted proper s-t-path, and the maximum weighted proper s-t-trail. When the minimization problems are considered we assume that (G, c, w) has no negative proper cycle, and when the maximization problems are considered we assume that (G, c, w) has no proper closed trail. We show that all these problems are solvable in polynomialtime. (C) 2019 Elsevier B.V. All rights reserved.
It is well known that general 0-1 programming problems are NP-Complete and their optimal solutions cannot be found with polynomial-time algorithms unless P=NP. In this paper, we identify a specific class of 0-1 progra...
详细信息
It is well known that general 0-1 programming problems are NP-Complete and their optimal solutions cannot be found with polynomial-time algorithms unless P=NP. In this paper, we identify a specific class of 0-1 programming problems that is polynomially solvable, and propose two polynomial-time algorithms to find its optimal solutions. This class of 0-1 programming problems commits to a wide range of real-world industrial applications. We provide an instance of representative in the field of supply chain management.
We revisit the classical resource allocation problem with general convex objective functions, subject to an integer knapsack constraint. This class of problems is fundamental in discrete optimization and arises in a w...
详细信息
We revisit the classical resource allocation problem with general convex objective functions, subject to an integer knapsack constraint. This class of problems is fundamental in discrete optimization and arises in a wide variety of applications. In this paper, we propose a novel polynomial-time divide-and-conquer algorithm (called the multi-phase algorithm) and prove that it has a computational complexity of O(n log n log N), which outperforms the best known polynomial-time algorithm with O(n( log N)(2)). (C) 2015 Elsevier B.V. All rights reserved.
We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates of detection. Our ana...
详细信息
We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates of detection. Our analysis relies on the study of the number of satisfying assignments, for which we prove new results. We also address algorithmic issues, and give a computationally efficient test with optimal statistical performance. This result is compared to an average-case hypothesis on the hardness of refuting satisfiability of random formulas.
In this paper, we study the scheduling of proportional-linearly deteriorating jobs with positional due indices, release dates, deadlines and precedence relations on a single machine. The scheduling criteria studied in...
详细信息
In this paper, we study the scheduling of proportional-linearly deteriorating jobs with positional due indices, release dates, deadlines and precedence relations on a single machine. The scheduling criteria studied in this paper include the makespan, maximum lateness, maximum tardiness, maximum flow time, maximum weighted completion time, maximum scheduling cost, total completion time, and the number of tardy jobs. By applying Lawler's rule and Smith's rule, polynomially solvable problems are processed by using two unified methods. We also present some new NP-hardness results when processing times of the jobs have no deterioration. Our results generalize a series of known achievements in the literature.
This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, c...
详细信息
This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, community detection and hypothesis testing. For each problem, we review state-of-the-art results in the literature followed by general principles behind the optimal procedures that lead to minimax estimation and testing. This allows us to connect problems in network analysis to other statistical inference problems from a general perspective.
暂无评论