An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of ...
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An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters and pairwise co-occurrence. The method is based on subset convolution and yields the posterior distribution for the number of clusters in O(n3(n)) operations or O(n(3)2(n)) using fast subset convolution. Pairwise co-occurrence probabilities are then obtained in O(n(3)2(n)) operations. This is considerably faster than exhaustive enumeration of all partitions.
We focus on a threat scenario where a terrorist would utilize a small vessel to attack a maritime target. We consider how to place multiple types of detectors to protect maritime targets from such an attack. Detectors...
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We focus on a threat scenario where a terrorist would utilize a small vessel to attack a maritime target. We consider how to place multiple types of detectors to protect maritime targets from such an attack. Detectors are not perfectly reliable. The resulting detector placement problem is formulated as a nonlinear binary integer program such that the expected damage cost caused by the small vessel attack is minimized. Two exact algorithms and a greedy adding heuristic are proposed. Moreover, we conduct a detailed computational study and provide a case study in New York Harbor. (C) 2016 Elsevier Ltd. All rights reserved.
An author's profile on Google Scholar consists of indexed articles and associated data, such as the number of citations and the H-index. The author is allowed to merge articles;this may affect the H-index. We anal...
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An author's profile on Google Scholar consists of indexed articles and associated data, such as the number of citations and the H-index. The author is allowed to merge articles;this may affect the H-index. We analyze the (parameterized) computational complexity of maximizing the H-index using article merges. Herein, to model realistic manipulation scenarios, we define a compatibility graph whose edges correspond to plausible merges. Moreover, we consider several different measures for computing the citation count of a merged article. For the measure used by Google Scholar, we give an algorithm that maximizes the H-index in linear time if the compatibility graph has constant-size connected components. In contrast, if we allow to merge arbitrary articles (that is, for compatibility graphs that are cliques), then already increasing the H-index by one is NP-hard. Experiments on Google Scholar profiles of AI researchers show that the H-index can be manipulated substantially only if one merges articles with highly dissimilar titles. (C) 2016 Elsevier B.V. All rights reserved.
Our goal is to show tight bounds on the running time of algorithms for scheduling and packing problems. To prove lower bounds, we investigate implications of the exponential time hypothesis on such algorithms. For exa...
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Our goal is to show tight bounds on the running time of algorithms for scheduling and packing problems. To prove lower bounds, we investigate implications of the exponential time hypothesis on such algorithms. For exact algorithms we consider the dependence of the running time on the number n of items (for packing) or jobs (for scheduling). We prove a lower bound of 2(o(n)) x vertical bar vertical bar I vertical bar vertical bar(O(n)), where vertical bar vertical bar I vertical bar vertical bar denotes the encoding length of the instance, for several of these problems, including SUBSETSUM, KNAPSACK, BINPACKING, < P2 vertical bar vertical bar C-max >, and < P2 vertical bar vertical bar Sigma w(j)C(j)>. We also develop an algorithmic framework that is able to solve a large number of scheduling and packing problems in time 2o(n) x vertical bar vertical bar I vertical bar vertical bar(O(n)). Finally, we consider approximation schemes. We show that there is no polynomial time approximation scheme for MULTIPLEKNAPSACK (MKS) and 2D-KNAPSACK with running time 2(o(1/epsilon)) x vertical bar vertical bar I vertical bar vertical bar(O(n)) and n(o(1/epsilon)) x vertical bar vertical bar I vertical bar vertical bar(O(n)), respectively.
Given a set of n points on a line, where each point has one of k colors, and given an integer si >= 1 for each color i, 1 = 1. We also obtain some interesting results for the general problem SCSI-t. From the negati...
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Given a set of n points on a line, where each point has one of k colors, and given an integer si >= 1 for each color i, 1 <= i <= k, the problem SHORTEST COLOR-SPANNING t INTERVALS (SCSI-t) aims at finding t intervals to cover at least si points of each color i, such that the maximum length of the intervals is minimized. Chen and Misiolek introduced the problem SCSI-1, and presented an algorithm running in O(n) time if the input points are sorted. Khanteimouri et al. gave an O (n(2) logn) time algorithm for the special case of SCSI-2 with s(i) = 1 for all colors i. In this paper, we present an improved algorithm with running time of 0(n2) for SCSI-2 with arbitrary si >= 1. We also obtain some interesting results for the general problem SCSI-t. From the negative direction, we show that approximating SCSI-t within any ratio is NP-hard when t is part of the input, is W[2]-hard when t is the parameter, and is W[1]-hard with both t and k as parameters. Moreover, the NP-hardness and the W[2]-hardness with parameter t hold even if si = 1 for all i. From the positive direction, we show that SCSI-t with si = 1 for all i is fixed-parameter tractable with k as the parameter, and admits an exact algorithm running in 0 (2(k)n . max{k, logn}) time. (C) 2015 Elsevier B.V. All rights reserved.
Reversible logic has gained interest of researchers worldwide for its ultra-low power and high speed computing abilities in the future quantum information processing. Testing of these circuits is important for ensurin...
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Reversible logic has gained interest of researchers worldwide for its ultra-low power and high speed computing abilities in the future quantum information processing. Testing of these circuits is important for ensuring high reliability of their operation. In this work, we propose an ATPG algorithm for reversible circuits using an exact approach to generate CTS (Complete Test Set) which can detect single stuck-at faults, multiple stuck-at faults, repeated gate fault, partial and complete missing gate faults which are very useful logical fault models for reversible logic to model any physical defect. Proposed algorithm can be used to test a reversible circuit designed with k-CNOT, Peres and Fredkin gates. Through extensive experiments, we have validated our proposed algorithm for several benchmark circuits and other circuits with family of reversible gates. This algorithm produces a minimal and complete test set while reducing test generation time as compared to existing state-of-the-art algorithms. A testing tool is developed satisfying the purpose of generating all possible CTS's indicating the simulation time, number of levels and gates in the circuit. This paper also contributes to the detection and removal of redundant faults for optimal test set generation.
We consider a scenario in which certain target locations are monitored through sensors, which are scattered all over a considered area. A quality-of-service threshold imposes that, at any given time, a predefined perc...
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We show that the 3-colorability problem can be solved in O(1.296(n)) time on any n-vertex graph with minimum degree at least 15. This algorithm is obtained by constructing a dominating set of the graph greedily, enume...
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We show that the 3-colorability problem can be solved in O(1.296(n)) time on any n-vertex graph with minimum degree at least 15. This algorithm is obtained by constructing a dominating set of the graph greedily, enumerating all possible 3-colorings of the dominating set, and then solving the resulting 2-list coloring instances in polynomial time. We also show that a 3-coloring can be obtained in 2(o(n)) time for graphs having minimum degree at least w(n) where w(n) is any function which goes to infinity. We also show that if the lower bound on minimum degree is replaced by a constant (however large it may be), then neither a 2(o(n)) time nor a 2(o(m)) time algorithm is possible (m denotes the number of edges) for 3-colorability unless Exponential Time Hypothesis (ETH) fails. We also describe an algorithm which obtains a 4-coloring of a 3-colorable graph in O(1.2535(n)) time. (C) 2010 Elsevier B.V. All rights reserved.
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank ...
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ISBN:
(纸本)9781450343800
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active, this is a non-convex optimization problem, otherwise it is a semidefinite program. Both find numerous applications especially in systems control theory and combinatorial optimization, but even in more general contexts such as polynomial optimization or real algebra. While numerical algorithms exist for solving this problem, such as interior-point or Newton-like algorithms, in this paper we propose an approach based on symbolic computation. We design an exact algorithm for solving rank-constrained semidefinite programs, whose complexity is essentially quadratic on natural degree bounds associated to the given optimization problem: for subfamilies of the problem where the size of the feasible matrix is fixed, the complexity is polynomial in the number of variables. The algorithm works under assumptions on the input data: we prove that these assumptions are generically satisfied. We also implement it in Maple and discuss practical experiments.
In this paper, we study the Shortest Color Spanning Intervals problem, and related generalizations, namely Smallest Color Spanning t Squares and Smallest Color Spanning t Circles. The generic setting is the following:...
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ISBN:
(纸本)9783319292212;9783319292205
In this paper, we study the Shortest Color Spanning Intervals problem, and related generalizations, namely Smallest Color Spanning t Squares and Smallest Color Spanning t Circles. The generic setting is the following: we are given n points in the plane (or on the line), each colored with one of k colors, and for each color i we also have a demand si. Given a budget t, we are required to find at most t objects (for example, intervals, squares, circles, etc.) that cover at least si points of color i. Typically, the goal is to minimize the maximum perimeter or area. We provide exact algorithms for these problems for the cases of intervals, circles and squares, generalizing several known results. In the case of intervals, we provide a comprehensive understanding of the complexity landscape of the problem after taking several natural parameters into account. Given that the problem turns out to be W[1]-hard parameterized by the standard parameters, we introduce a new parameter, namely sparsity, and prove new hardness and tractability results in this context. For squares and circles, we use existing algorithms of one smallest color spanning object in order to design algorithms for getting t identical objects of minimum size whose union spans all the colors.
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