We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem (LHP). It is shown...
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We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem (LHP). It is shown that the LHP for TIM on degree-3 graphs is equivalent modulo polynomial reductions to the LHP for general k-local 'stoquastic' Hamiltonians with any constant . This result implies that estimating the ground state energy of TIM on degree-3 graphs is a complete problem for the complexity class -an extension of the classical class . As a corollary, we complete the complexity classification of 2-local Hamiltonians with a fixed set of interactions proposed recently by Cubitt and Montanaro. Secondly, we study quantum annealing algorithms for finding ground states of classical spin Hamiltonians associated with hard optimization problems. We prove that the quantum annealing with TIM Hamiltonians is equivalent modulo polynomial reductions to the quantum annealing with a certain subclass of k-local stoquastic Hamiltonians. This subclass includes all Hamiltonians representable as a sum of a k-local diagonal Hamiltonian and a 2-local stoquastic Hamiltonian.
We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, w...
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We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted, medium-restricted, or group-separable profiles. We measure this distance by the number of voters or alternatives that have to be deleted to make the profile a nicely structured one. Our results classify the problem variants with respect to their computational complexity, and draw a clear line between computationally tractable (polynomial-time solvable) and computationally intractable (NP-hard) questions. (C) 2015 Elsevier B.V. All rights reserved.
In 2015, Bau and Dankelmann showed that every bridgeless graph G of order n and minimum degree 8 has an orientation of diameter at most 11 n/delta+1 + 9. As they were convinced that this bound is not best possible, th...
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In 2015, Bau and Dankelmann showed that every bridgeless graph G of order n and minimum degree 8 has an orientation of diameter at most 11 n/delta+1 + 9. As they were convinced that this bound is not best possible, they posed the problem of improving it. In this paper, we prove that such a graph G has an orientation of diameter less than 7n/delta+1 and give a polynomial-time algorithm to construct one. (C) 2016 Elsevier Ltd. All rights reserved.
We study end-to-end routing in a communication system where there is a bandwidth and a propagation delay associated with each link, as well as a queuing delay associated with each intermediate node. We present a polyn...
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We study end-to-end routing in a communication system where there is a bandwidth and a propagation delay associated with each link, as well as a queuing delay associated with each intermediate node. We present a polynomialtime algorithm for computing an optimal multichannel routing to transmit a given message. Examples are also given to show that several previously published path-based algorithms for this problem are suboptimal. We then generalize the multichannel routing problem to delay-constrained multichannel routing problem and show that this generalized problem can also be solved in polynomialtime. (C) 2002 Elsevier Science B.V. All rights reserved.
Given an undirected graph G = (V, E), it is known that its edge-connectivity lambda(G) can be computed by solving O(\V\) max-flow problems. The best time bounds known for the problem are O(lambda(G)\V\2), due to Matul...
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Given an undirected graph G = (V, E), it is known that its edge-connectivity lambda(G) can be computed by solving O(\V\) max-flow problems. The best time bounds known for the problem are O(lambda(G)\V\2), due to Matula (28th IEEE Symposium on the Foundations of Computer Science, 1987, pp. 249-251) if G is simple, and O(\E\3/2\V\), due to Even and Tarjan (SIAM J. Comput., 4 (1975), pp. 507-518) if G is multiple. An O(\E\ + min {lambda(G)\V\2, p\V\ + \V\2 log \V\}) time algorithm for computing the edge-connectivity lambda(G) of a multigraph G = (V, E), where p(less-than-or-equal-to \E\) is the number of pairs of nodes between which G has an edge, is proposed. This algorithm does not use any max-flow algorithm but consists only of \V\ times of graph searches and edge contractions. This method is then extended to a capacitated network to compute its minimum cut capacity in O(\V\\E\ + \V\2 log\V\) time.
We study the following two graph modification problems: given a graph G and an integer k, decide whether G can be transformed into a tree or into a path, respectively, using at most k edge contractions. These problems...
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We study the following two graph modification problems: given a graph G and an integer k, decide whether G can be transformed into a tree or into a path, respectively, using at most k edge contractions. These problems, which we call TREE CONTRACTION and PATH CONTRACTION, respectively, are known to be NP-complete in general. We show that on chordal graphs these problems can be solved in 0(n + m) and 0(nm) time, respectively. As a contrast, both problems remain NP-complete when restricted to bipartite input graphs. (C) 2013 Elsevier B.V. All rights reserved.
In this paper, the strategies for acceleration of the path-following polynomialtime interior point method for linear and linearly constrained quadratic programming problems are studied. These strategies are based on ...
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In this paper, the strategies for acceleration of the path-following polynomialtime interior point method for linear and linearly constrained quadratic programming problems are studied. These strategies are based on (i) exploiting the results of computations done at the previous iterations (Karmarkar's acceleration scheme and a scheme based on the preconditioned conjugate gradient method);(ii) implementation of "fast" linear algebra routines;(iii) parallel computations.
This paper considers the minimum connection problem in networks with uncertain data. In such a network it is assumed that one can establish a link e by paying a cost c(e) in a given interval [c(e)(-), c(e)(+)] while t...
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This paper considers the minimum connection problem in networks with uncertain data. In such a network it is assumed that one can establish a link e by paying a cost c(e) in a given interval [c(e)(-), c(e)(+)] while taking a risk (c(e)(+) - c(e))/(c(e)(+) - c(e)(-)) of link failure. We develop polynomial time algorithms for minimum cost network connection with paths or spanning trees under risk-sum constraints. (C) 2009 Elsevier B.V. All rights reserved.
In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number and the harmonious chromatic number of P4-tidy graphs and (q,q-4)-graphs, for every fixed q. The...
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In this paper, we give new sparse interpolation algorithms for black box polynomial f whose coefficients are from a finite set. In the univariate case, we recover f from one evaluation f (/3) for a sufficiently large ...
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ISBN:
(数字)9783319663203
ISBN:
(纸本)9783319663203;9783319663197
In this paper, we give new sparse interpolation algorithms for black box polynomial f whose coefficients are from a finite set. In the univariate case, we recover f from one evaluation f (/3) for a sufficiently large number /3. In the multivariate case, we introduce the modified Kronecker substitution to reduce the interpolation of a multivariate polynomial to that of the univariate case. Both algorithms have polynomial bit -size complexity.
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