Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagion in a graph;the lower the burning nu...
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Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagion in a graph;the lower the burning number, the faster the contagion spreads. We prove that the corresponding graph decision problem is NP-complete when restricted to acyclic graphs with maximum degree three, spider graphs and path-forests. We provide polynomial time algorithms for finding the burning number of spider graphs and path forests if the number of arms and components, respectively, are fixed. Finally, we describe a polynomialtime approximation algorithm with approximation factor 3 for general graphs. (C) 2017 Elsevier B.V. All rights reserved.
A recently introduced lot scheduling problem is considered. It is to find a partition of jobs of n orders into lots and to sequence these lots on a single machine so that the total average completion time of the order...
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A recently introduced lot scheduling problem is considered. It is to find a partition of jobs of n orders into lots and to sequence these lots on a single machine so that the total average completion time of the orders is minimized. A simple O(n log n) timealgorithm is presented for this problem in the literature, with a relatively sophisticated proof of its optimality. We show that modeling this problem as a classic batching machine problem makes its optimal solution obvious.
This paper deals with the reconstruction of special cases of binary matrices with adjacent 1s. Each element is horizontally adjacent to at least another element. The projections are the number of elements on each row ...
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ISBN:
(纸本)9783319591087;9783319591070
This paper deals with the reconstruction of special cases of binary matrices with adjacent 1s. Each element is horizontally adjacent to at least another element. The projections are the number of elements on each row and column. We give a greedy polynomial time algorithm to reconstruct such matrices when satisfying only the vertical projection. We show also that the reconstruction is NP-complete when fixing the number of sequence of length two and three per row and column.
Auction-based service provisioning and resource allocation have demonstrated strong potential in Cloud-RAN wireless network architecture and heterogeneous networks for effective resource sharing. One major technical c...
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ISBN:
(纸本)9781509050192
Auction-based service provisioning and resource allocation have demonstrated strong potential in Cloud-RAN wireless network architecture and heterogeneous networks for effective resource sharing. One major technical challenge is the integration of interference constraints in auction-based solutions. In this work we transform the interference constraint requirement into a set of linear constraints on each cluster. We tackle the generally NP-hard clustering problem by developing a novel practical suboptimal solution that can meet our design requirement. Our novel algorithm utilizes the properties of chordal graphs and applies Lexicographic Breadth First Search (Lex-BFS) algorithm for cluster splitting. This polynomialtime approximate algorithm searches for maximal cliques in a graph by generating strong performance in terms of subgraph density and probability of optimal clustering without suffering from the high complexity of the optimal solution.
Graph isomorphism is an important problem in graph theory.A popular class of testing methods uses necessary conditions to refine the vertex partition iteratively with ***,these known algorithms need many more backtrac...
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Graph isomorphism is an important problem in graph theory.A popular class of testing methods uses necessary conditions to refine the vertex partition iteratively with ***,these known algorithms need many more backtracking operations so as to construct a search tree for testing and pruning which results in exponential time cost in the worst *** partition property of a necessary condition plays the key role in determining the efficiency of this kind *** on a more effective necessary condition we proposed previously,this paper develops an O(n 4) algorithm for undirected graph isomorphism using vertex partition and *** algorithm takes advantage of the intersecting operation on the vertex match set and the recursive property of the graph isomorphism resulting in the subgraph *** experiments on the Graph Database validated the correctness and the efficiency of this algorithm for graph isomorphism.
In a partial inverse matroid problem, given a matroid M = (S, I), a real valued weight function w on S, and an independent set I-0 is an element of I, the goal is to modify the weight w as small as possible to a new w...
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In a partial inverse matroid problem, given a matroid M = (S, I), a real valued weight function w on S, and an independent set I-0 is an element of I, the goal is to modify the weight w as small as possible to a new weight (w) over bar such that there exists a (w) over bar -maximum base containing I-0. In this paper, we study a constraint version of the partial inverse matroid problem in which the weight can only be decreased. A polynomial time algorithm is presented under I-infinity-norm. (C) 2016 Elsevier B.V. All rights reserved.
The complexity of the equation solvability problem is known for nilpotent groups, for not solvable groups and for some semidirect products of Abelian groups. We provide a new polynomial time algorithm for deciding the...
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The complexity of the equation solvability problem is known for nilpotent groups, for not solvable groups and for some semidirect products of Abelian groups. We provide a new polynomial time algorithm for deciding the equation solvability problem over certain semidirect products, where the first factor is not necessarily Abelian. Our main idea is to represent such groups as matrix groups, and reduce the original problem to equation solvability over the underlying field. Further, we apply this new method to give a much more efficient algorithm for equation solvability over nilpotent rings than previously existed.
In a finite undirected graph G = (V, E), a vertex v is an element of V dominates itself and its neighbors in G. A vertex set D subset of V is an efficient dominating set (e.d.s. for short) of G if every v 2 V is domin...
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In a finite undirected graph G = (V, E), a vertex v is an element of V dominates itself and its neighbors in G. A vertex set D subset of V is an efficient dominating set (e.d.s. for short) of G if every v 2 V is dominated in G by exactly one vertex of D. The Efficient Domination (ED) problem, which asks for the existence of an e.d.s. in G, is known to be NP-complete for P-7-free graphs and solvable in polynomialtime for P-5-free graphs. The P-6-free case was the last open question for the complexity of ED on F-free graphs. Recently, Lokshtanov, Pilipczuk, and van Leeuwen showed that weighted ED is solvable in polynomialtime for P-6-free graphs, based on their quasi-polynomialalgorithm for the Maximum Weight Independent Set problem for P-6-free graphs. Independently, by a direct approach which is simpler and faster, we found an O(n(5)m) time solution for weighted ED on P-6-free graphs. Moreover, we show that weighted ED is solvable in linear time for P-5-free graphs which solves another open question for the complexity of (weighted) ED. The result for P-5-free graphs is based on modular decomposition.
This paper studies a k-median Steiner forest problem that jointly optimizes the opening of at most k facility locations and their connections to the client locations, so that each client is connected by a path to an o...
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This paper studies a k-median Steiner forest problem that jointly optimizes the opening of at most k facility locations and their connections to the client locations, so that each client is connected by a path to an open facility, with the total connection cost minimized. The problem has wide applications in the telecommunication and transportation industries, but is strongly NP-hard. In the literature, only a 2-approximation algorithm is known, it being based on a Lagrangian relaxation of the problem and using a sophisticated primal-dual schema. In this study, we have developed an improved approximation algorithm using a simple transformation from an optimal solution of a minimum spanning tree problem. Compared with the existing 2-approximation algorithm, our new algorithm not only achieves a better approximation ratio that is easier to be proved, but also guarantees to produce solutions of equal or better quality up to 50 percent improvement in some cases. In addition, for two non-trivial special cases, where either every location contains a client, or all the locations are in a tree-shaped network, we have developed, for the first time in the literature, new algorithms that can solve the problem to optimality in polynomialtime. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance matrix under the assumption...
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extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance matrix under the assumption that this eigenvector is sparse. An impressive range of estimators have been proposed;some of these are fast to compute, while others are known to achieve the mini-max optimal rate over certain Gaussian or sub-Gaussian classes. In this paper, we show that, under a widely-believed assumption from computational complexity theory, there is a fundamental trade-off between statistical and computational performance in this problem. More precisely, working with new, larger classes satisfying a restricted covariance concentration condition, we show that there is an effective sample size regime in which no randomised polynomial time algorithm can achieve the minimax optimal rate. We also study the theoretical performance of a (polynomialtime) variant of the well-known semidefinite relaxation estimator, revealing a subtle interplay between statistical and computational efficiency.
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