Random Duplicated Assignment (RDA) is an approach in which video data is stored by assigning a number of copies of each data block to different, randomly chosen disks. It has been shown that this approach results in s...
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Random Duplicated Assignment (RDA) is an approach in which video data is stored by assigning a number of copies of each data block to different, randomly chosen disks. It has been shown that this approach results in smaller response times and lower disk and RAM costs compared to the well-known disk stripping techniques. Based on this storage approach, one has to determine, for each given batch of data blocks, from which disk each of the data blocks is to be retrieved. This is to be done in such a way that the maximum load of the disks is minimized. The problem is called the Retrieval Selection Problem (RSP). In this paper, we propose a new efficient algorithm for RSP. This algorithm is based on the breadth-first search approach and is able to guarantee optimal solutions for RSP in O(n(2) + mn), where m and n correspond to the number of data blocks and the number of disks, respectively. We will show that our proposed algorithm has a lower time complexity than an existing algorithm, called the MFS algorithm. (C) 2002 Elsevier Science B.V. All rights reserved.
Given two graphs H1 and H2, a graph is (H1, H2)-free if it contains no induced subgraph isomorphic to H1 or H2. Let Pt be the path on t vertices. A bull is the graph obtained from a triangle with two disjoint pendant ...
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Given two graphs H1 and H2, a graph is (H1, H2)-free if it contains no induced subgraph isomorphic to H1 or H2. Let Pt be the path on t vertices. A bull is the graph obtained from a triangle with two disjoint pendant edges. In this paper, we show that there are finitely many 5-vertex-critical (P5, bull)-free graphs.(c) 2023 Elsevier B.V. All rights reserved.
The computational complexity of the following problem is investigated: Given a permutation group specified as a set of generators, and a single target permutation which is a member of the group, what is the shortest e...
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The computational complexity of the following problem is investigated: Given a permutation group specified as a set of generators, and a single target permutation which is a member of the group, what is the shortest expression for the target permutation in terms of the generators? The general problem is demonstrated to be PSppace -complete and, indeed,is shown to remain so even when the generator set is restricted to contain only two permutations. The restriction on generator set cardinality is the best possible, as the problem becomes soluble in polynomialtime if the generator set cantains only one permutation. An interesting feature of this problem is that it does not fall under the headings of ‘two person games’ or ‘formal languages’ which cover the great majority of known PSpace -complete problems. Some restricted versions of the problem, in which the generator set is fixed rather than being part of the problem instance, are also investigated and shown to be computationally tractable. One result of this kind is that determining the most compact expression of a permutation in terms of ‘cyclicly adjacent transpositions’ can be achieved in polynomialtime. Thus, from an initial arrangement of distinct objects on a circle, one can quickly compute the smallest number of interchanges of adjacent objects required to realise any other arrangement. Surprisingly, this problem appears substantially more difficult to solve than the related one (for which a solution has been known for some time) in which the objects are arranged on a line segment.
We show that a modified variant of the interior point method can solve linear programs (LPs) whose coefficients are real numbers from a subring of the algebraic integers. By defining the encoding size of such numbers ...
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We show that a modified variant of the interior point method can solve linear programs (LPs) whose coefficients are real numbers from a subring of the algebraic integers. By defining the encoding size of such numbers to be the bit size of the integers that represent them in the subring, we prove the modified algorithm runs in timepolynomial in the encoding size of the input coefficients, the dimension of the problem, and the order of the subring. We then extend the Tardos scheme to our case, obtaining a running time which is independent of the objective and right-hand side data. As a consequence of these results, we are able to show that LPs with real circulant coefficient matrices can be solved in strongly polynomialtime. Finally, we show how the algorithm can be applied to LPs whose coefficients belong to the extension of the integers by a fixed set of square roots.
In this paper, we present new results in the area of reconfiguration of stateful interactive processes in the presence of faults. More precisely, we consider a set of servers/processes that have the same functionality...
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In this paper, we present new results in the area of reconfiguration of stateful interactive processes in the presence of faults. More precisely, we consider a set of servers/processes that have the same functionality, i.e., are able to perform the same tasks and provide the same set of services to their clients. In the case when several of them turn out to be faulty, we want to reconfigure the system so that the clients of the faulty servers/processes are served by some other, fault-free, servers of the system in a way that is transparent to all the system clients. We propose a new method for reconfiguring in the presence of faults: compensation paths. Compensation paths are an efficient way of shifting spare resources from where they are available to where they are needed. We also present optimal and suboptimal simple reconfiguration algorithms of low polynomialtime complexity O(nmlog(n(2)/m)) for the optimal and O(m) for the suboptimal algorithms, where M is the number of processes and m is the number of primary-backup relationships. The optimal algorithms compute the way to reconfigure the system whenever the reconfiguration is possible. The suboptimal algorithms may sometimes fail to reconfigure the system, although reconfiguration would be possible by using the optimal centralized algorithms. However, suboptimal algorithms have other competitive advantages over the centralized optimal algorithms with regard to time complexity and communication overhead.
This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient algorithm for computing ...
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This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient algorithm for computing the highest degree coefficients of the weighted Ehrhart quasi-polynomial for a rational simple polytope in varying dimension, when the weights of the lattice points are given by a polynomial function h. Our technique is based on a refinement of an algorithm of A. Barvinok in the unweighted case (i.e., ha parts per thousand 1). In contrast to Barvinok's method, our method is local, obtains an approximation on the level of generating functions, handles the general weighted case, and provides the coefficients in closed form as step polynomials of the dilation. To demonstrate the practicality of our approach, we report on computational experiments which show that even our simple implementation can compete with state-of-the-art software.
A siphon (or alternatively a structural deadlock) of a Petri net is defined as a 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 t...
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A siphon (or alternatively a structural deadlock) of a Petri net is defined as a 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. A minimal siphon is a siphon such that any proper subset is not a siphon. The results of the paper are as follows. (1) The problem of deciding whether or not a given Petri net has a minimum siphon (i.e., a minimum-cardinality minimal siphon) is NP-complete. (2) A polynomial-time algorithm to find, if any, a minimal siphon or even a maximal class of mutually disjoint minimal siphons of a general Petri net is proposed.
This paper focuses on single machine scheduling subject to inventory constraints. Jobs either add items to an inventory or remove items from that inventory. Jobs that have to remove items cannot be processed if the re...
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This paper focuses on single machine scheduling subject to inventory constraints. Jobs either add items to an inventory or remove items from that inventory. Jobs that have to remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine with the minimization of the total weighted completion time, the maximum lateness, and the number of tardy jobs, respectively, as objective and determine their computational complexity. Since the general versions of our problems turn out to be strongly NP-hard, we consider special cases by assuming that different jobs have certain parameter values in common. We determine the computational complexity for all special cases when the objective is either to minimize total completion time or to minimize maximum lateness and for several special cases when the objective is either to minimize total weighted completion time or to minimize the number of tardy jobs. (C) 2010 Elsevier BM. All rights reserved.
We propose a simple O(vertical bar n(5)/log n vertical bar L) algorithm for linear programming feasibility, that can be considered as a polynomial-time implementation of the relaxation method. Our work draws from Chub...
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We propose a simple O(vertical bar n(5)/log n vertical bar L) algorithm for linear programming feasibility, that can be considered as a polynomial-time implementation of the relaxation method. Our work draws from Chubanov's "Divide-and-Conquer" algorithm (Chubanov, 2012), with the recursion replaced by a simple and more efficient iterative method. A similar approach was used in a more recent paper of Chubanov (2013). (C) 2014 Elsevier B.V. All rights reserved.
A siphon-trap of a Petri net N is defined as a place set S with S-. = S-., where S-.={u\ N has an edge from u to a vertex of S} and S-. = {v\ N has an edge from a vertex of S to v}. A minimal siphon-trap is a siphon-t...
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A siphon-trap of a Petri net N is defined as a place set S with S-. = S-., where S-.={u\ N has an edge from u to a vertex of S} and S-. = {v\ N has an edge from a vertex of S to v}. A minimal siphon-trap is a siphon-trap such that any proper subset is not a siphon-trap. The following polynomial-time algorithms are proposed: 1. FDST for finding, if any, a minimal siphon-trap or even a maximal class of mutually disjoint minimal siphon-traps of a given Petri net;2. FDSTi that repeats FDST i times in order to extract more minimal siphon-traps than FDST. 3. STFM-T (STFM-T-i, respectively) which is a combination of the Fourier-Motzkin method and FDST (FDSTi) and which has high possibility of finding, if any, at least one minimal-support nonnegative integer invariant.
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