The maximum number of minimal dominating sets in a chordal graph on n vertices is known to be at most 1.6181(n). However, no example of a chordal graph with more than 1.4422(n) minimal dominating sets is known. In thi...
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The maximum number of minimal dominating sets in a chordal graph on n vertices is known to be at most 1.6181(n). However, no example of a chordal graph with more than 1.4422(n) minimal dominating sets is known. In this paper, we narrow this gap between the known upper and lower bounds by showing that the maximum number of minimal dominating sets in a chordal graph is at most 1.5214(n). (C) 2016 Elsevier B.V. All rights reserved.
The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables...
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The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the "weight", and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The Monte-Carlo algorithms are applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed. (c) 2006 Elsevier Inc. All rights reserved.
Designing a reliable network becomes a time-consuming task if it involves All-Terminal Reliability (ATR) calculation, which belongs to the class of NP-hard problems. To make this task easier to address, we propose a n...
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Designing a reliable network becomes a time-consuming task if it involves All-Terminal Reliability (ATR) calculation, which belongs to the class of NP-hard problems. To make this task easier to address, we propose a new algorithm to decide the ATR feasibility of a given network without performing exhaustive calculation. The proposed algorithm cumulatively updates the lower and upper bounds of the ATR using the set of subnetworks decomposed or branched from. Once the lower or upper bound reaches the predetermined ATR requirement, the feasibility of is determined. The proposed algorithm is characterized by four existing ATR calculation methods, which decompose or branch into multiple subnetworks. The four implementations of the proposed algorithm will be tested via computer experiments. The results show that the proposed algorithm can make feasibility decision dramatically faster. The arrangement of subnetworks that can improve the performance of the proposed algorithm is also discussed.
This paper contains some algorithms and recommendations that enable increasing efficiency of cumulative updating of all-terminal reliability for a network with unreliable links. The existence of cutnodes, 2-node cuts,...
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This paper contains some algorithms and recommendations that enable increasing efficiency of cumulative updating of all-terminal reliability for a network with unreliable links. The existence of cutnodes, 2-node cuts, and chains in a network structure can be used for faster calculations.
We propose a series of algorithms for solving abstract convex programming problems and prove convergence to the global solution of the problem. The algorithms use an approximation of the objective function by piecewis...
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We propose a series of algorithms for solving abstract convex programming problems and prove convergence to the global solution of the problem. The algorithms use an approximation of the objective function by piecewise-linear minorants.
We propose a new class of non-real-time deterministic pushdown automata (dpda's), named dpda's having the weak segmental property (WSP), and show that the equivalence problem is solvable for two dpda's, on...
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We propose a new class of non-real-time deterministic pushdown automata (dpda's), named dpda's having the weak segmental property (WSP), and show that the equivalence problem is solvable for two dpda's, one of which is in this class. The equivalence checking algorithm to prove this problem is a further extended direct branching algorithm of Tomita;and with the new skipping step combined with the type B' replacement of Oyamaguchi, Inagaki and Honda. The algorithm is still relatively simple. The class of dpda's given above is one of the widest known subclasses of proper dpda's (introduced by Ukkonen);with the decidable extended equivalence problem.
Treedepth is a well-established width measure which has recently seen a resurgence of interest. Since graphs of bounded treedepth are more restricted than graphs of bounded treeor pathwidth, we are interested in the a...
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Treedepth is a well-established width measure which has recently seen a resurgence of interest. Since graphs of bounded treedepth are more restricted than graphs of bounded treeor pathwidth, we are interested in the algorithmic utility of this additional structure. On the negative side, we show with a novel approach that the space consumption of any (single-pass) dynamic programming algorithm on treedepth decompositions of depth d cannot be bounded by (2 e) d logO (1) n for VERTEX COVER, (3 e) d logO (1) n for 3-COLORING and (3 e) d logO (1) n for DOMINATING SET for any e > 0. This formalizes the common intuition that dynamic programming algorithms on graph decompositions necessarily consume a lot of space and complements known results of the time-complexity of problems restricted to low-treewidth classes. We then show that treedepth lends itself to the design of branching algorithms. Specifically, we design two novel algorithms for DOMINATING SET on graphs of treedepth d: A pure branching algorithm that runs in time dO (d2) n and uses space O (d3 log d + d log n) and a hybrid of branching and dynamic programming that achieves a running time of O (3d log d n) while using O (2dd log d + d log n) space.
The Hamiltonian cycle problem consists of finding a cycle in a given graph that passes through every single vertex exactly once, or determining that this cannot be achieved. In this investigation, a graph is considere...
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The Hamiltonian cycle problem consists of finding a cycle in a given graph that passes through every single vertex exactly once, or determining that this cannot be achieved. In this investigation, a graph is considered with an associated set of matrices. The entries of each of the matrix correspond to a different weight of an arc. A multi-objective Hamiltonian cycle problem is addressed here by computing a Pareto set of solutions that minimize the sum of the weights of the arcs for each objective. Our heuristic approach extends the Branch-and-Fix algorithm, an exact method that embeds the problem in a stochastic process. To measure the efficiency of the proposed algorithm, we compare it with a multi-objective genetic algorithm in graphs of a different number of vertices and density. The results show that the density of the graphs is critical when solving the problem. The multi-objective genetic algorithm performs better (quality of the Pareto sets) than the proposed approach in random graphs with high density;however, in these graphs it is easier to find Hamiltonian cycles, and they are closer to the multi-objective traveling salesman problem. The results reveal that, in a challenging benchmark of Hamiltonian graphs with low density, the proposed approach significantly outperforms the multi-objective genetic algorithm.
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