Weconsider the largest number of minimal separators a graph on n vertices can have. - We give a new proof that this number is in O((1+root 5/2)(n).n). We prove that this number is in omega(1.4457(n)), improving on the...
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Weconsider the largest number of minimal separators a graph on n vertices can have. - We give a new proof that this number is in O((1+root 5/2)(n).n). We prove that this number is in omega(1.4457(n)), improving on the previous best lower bound of Omega(3(n/3)) subset of omega(1.4422(n)). This gives also an improved lower bound on the number of potential maximal cliques in a graph. We would like to emphasize that our proofs are short, simple, and elementary.
The dualization in arbitrary posets is a well-studied problem in combinatorial enumeration and is a crucial step in many applications in logics, databases, artificial intelligence and pattern mining. The objective of ...
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The dualization in arbitrary posets is a well-studied problem in combinatorial enumeration and is a crucial step in many applications in logics, databases, artificial intelligence and pattern mining. The objective of this paper is to study reductions of the dualization problem on arbitrary posets to the dualization problem on boolean lattices, for which output quasi-polynomial time algorithms exist, Quasi-polynomial time algorithms are algorithms which run in no(logn) where n is the size of the input and output. We introduce convex embedding and poset reflection as key notions to characterize such reductions. As a consequence, we identify posets, which are not boolean lattices, for which the dualization problem remains in quasi-polynomial time and propose a classification of posets with respect to dualization. From these results, we study how they can be applied to maximal pattern mining problems. We deduce a new classification of pattern mining problems and we point out how known problems involving sequences and conjunctive queries patterns, fit into this classification. Finally, we explain how to adapt the seminal DUALIZE & ADVANCE algorithm to deal with such patterns. As far as we know, this is the first contribution to explicit non-trivial reductions for studying the hardness of maximal pattern mining problems and to extend the DUALIZE & ADVANCE algorithm for complex patterns. (C) 2016 Elsevier B.V. All rights reserved.
Due to the sheer size of real-world networks, delay and space become quite relevant measures for the cost of enumeration in network analytics. This paper presents efficient algorithms for listing maximum cliques in ne...
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In this paper, we address three related problems. One is the enumeration of all the maximal edge induced chain subgraphs of a bipartite graph, for which we provide a polynomial delay algorithm. We give bounds on the n...
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ISBN:
(纸本)9783319445434;9783319445427
In this paper, we address three related problems. One is the enumeration of all the maximal edge induced chain subgraphs of a bipartite graph, for which we provide a polynomial delay algorithm. We give bounds on the number of maximal chain subgraphs for a bipartite graph and use them to establish the input-sensitive complexity of the enumeration problem. The second problem we treat is the one of finding the minimum number of chain subgraphs needed to cover all the edges a bipartite graph. For this we provide an exact exponential algorithm with a non trivial complexity. Finally, we approach the problem of enumerating all minimal chain subgraph covers of a bipartite graph and show that it can be solved in quasi-polynomial time.
Background: The problem of enumerating bubbles with length constraints in directed graphs arises in transcriptomics where the question is to identify all alternative splicing events present in a sample of mRNAs sequen...
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Background: The problem of enumerating bubbles with length constraints in directed graphs arises in transcriptomics where the question is to identify all alternative splicing events present in a sample of mRNAs sequenced by RNA-seq. Results: We present a new algorithm for enumerating bubbles with length constraints in weighted directed graphs. This is the first polynomial delay algorithm for this problem and we show that in practice, it is faster than previous approaches. Conclusion: This settles one of the main open questions from Sacomoto et al. (BMC Bioinform 13: 5, 2012). Moreover, the new algorithm allows us to deal with larger instances and possibly detect longer alternative splicing events.
Submodular functions are powerful tools to model and solve either to optimality or approximately many operational research problems including problems defined on graphs. After reviewing some long-standing theoretical ...
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Submodular functions are powerful tools to model and solve either to optimality or approximately many operational research problems including problems defined on graphs. After reviewing some long-standing theoretical results about the structure of local and global maxima of submodular functions, Cherenin's selection rules and his Dichotomy Algorithm, we revise the above mentioned theory and show that our revision is useful for creating new non-binary branching algorithms and finding either approximation solutions with guaranteed accuracy or exact ones. (C) 2008 Elsevier B.V. All rights reserved.
The number of minimal dominating sets that a graph on n vertices can have is known to be at most 1.7159(n). This upper bound might not be tight, since no examples of graphs with 1.5705(n) or more minimal dominating se...
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The number of minimal dominating sets that a graph on n vertices can have is known to be at most 1.7159(n). This upper bound might not be tight, since no examples of graphs with 1.5705(n) or more minimal dominating sets are known. For several classes of graphs, we substantially improve the upper bound on the number of minimal dominating sets. At the same time, we give algorithms for enumerating all minimal dominating sets, where the running time of each algorithm is within a polynomial factor of the proved upper bound for the graph class in question. In several cases, we provide examples of graphs containing the maximum possible number of minimal dominating sets for graphs in that class, thereby showing the corresponding upper bounds to be tight. (C) 2013 Elsevier B.V. All rights reserved.
RFD (Reverse flow divert) set is a kind of maintenance-free delivery system driving by compress-air. It intermittently discharges through its delivery pipe. Without moving part, the optimized design of RFD set is a cr...
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ISBN:
(纸本)9781510804159
RFD (Reverse flow divert) set is a kind of maintenance-free delivery system driving by compress-air. It intermittently discharges through its delivery pipe. Without moving part, the optimized design of RFD set is a critical technical for efficient and stable operation. The deficiencies of traditional enumeration algorithms and marginal utility method have been indicated. Then, as the main point of the paper, Genetic Algorithm is discussed to solve the multi-objective and multidimensional optimization problem. By comparing the results of the three optimization methods, we can have the superiority of GA. Based on the needs of flow and head in industry, serial design of RFD has been made by using GA, thus the relationships of the structural parameters and operational parameters have been analyzed. The conversion relationship between different density and viscosity in average flow has been provided, which will be beneficial for the RFD set design in industry.
This paper provides a recursive enumeration algorithm for solving the nonconvex dynamic DEA models, to obtain cost minimum under nonconvex technologies. The validity of the algorithm is proved through some theorems. A...
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This paper provides a recursive enumeration algorithm for solving the nonconvex dynamic DEA models, to obtain cost minimum under nonconvex technologies. The validity of the algorithm is proved through some theorems. An illustrative example as well as a computational discussion are given to demonstrate the advantages of the proposed algorithm.
We study algorithmic techniques that produce the best K solutions to an instance of a parameterized NP-hard problem whose solutions are associated with a scoring function. Our parameterized top-K algorithms proceed in...
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We study algorithmic techniques that produce the best K solutions to an instance of a parameterized NP-hard problem whose solutions are associated with a scoring function. Our parameterized top-K algorithms proceed in two stages. The first stage is a structure algorithm that on a problem instance constructs a structure of feasible size, and the second stage is an enumerating algorithm that produces the K best solutions to the instance based on the structure. We show that many algorithm-design techniques for parameterized algorithms, such as branch-and-search, color coding, and bounded treewidth, can be adopted for designing efficient structure algorithms. We then develop new techniques that support efficient enumerating algorithms. In particular, we show that for a large class of well-known NP optimization problems, there are parameterized top-K algorithms that produce the best K solutions for the problems in feasible amount of average time per solution when the parameter value is small. Finally, we investigate the relation between fixed-parameter tractability and parameterized top-K algorithms. (C) 2012 Elsevier B.V. All rights reserved.
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