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检索条件"主题词=combinatorial algorithms"

共 172 条记录，以下是141-150 订阅

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Binary Matrix Completion Under Diameter Constraints 38

Binary Matrix Completion Under Diameter Constraints

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38th International Symposium on Theoretical Aspects of Computer Science (STACS)

作者： Koana, Tomohiro Froese, Vincent Niedermeier, Rolf Tech Univ Berlin Fac 4 Algorithm & Computat Complex Berlin Germany

ISBN: (纸本)9783959771801

We thoroughly study a novel but basic combinatorial matrix completion problem: Given a binary incomplete matrix, fill in the missing entries so that the resulting matrix has a specified maximum diameter (that is, upper-bounding the maximum Hamming distance between any two rows of the completed matrix) as well as a specified minimum Hamming distance between any two of the matrix rows. This scenario is closely related to consensus string problems as well as to recently studied clustering problems on incomplete data. We obtain an almost complete picture concerning the complexity landscape (P vs NP) regarding the diameter constraints and regarding the number of missing entries per row of the incomplete matrix. We develop polynomial-time algorithms for maximum diameter three, which are based on Deza's theorem [Discret. Math. 1973, J. Comb. Theory, Ser. B 1974] from extremal set theory. In this way, we also provide one of the rare links between sunflower techniques and stringology. On the negative side, we prove NP-hardness for diameter at least four. For the number of missing entries per row, we show polynomial-time solvability when there is only one missing entry and NP-hardness when there can be at least two missing entries. In general, our algorithms heavily rely on Deza's theorem and the correspondingly identified sunflower structures pave the way towards solutions based on computing graph factors and solving 2-SAT instances.

关键词： sunflowers binary matrices Hamming distance stringology consensus problems complexity dichotomy combinatorial algorithms graph factors 2-Sat Hamming radius

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A strongly polynomial algorithm for generalized flow maximization 14

A strongly polynomial algorithm for generalized flow maximiz...

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46th Annual ACM Symposium on Theory of Computing (STOC)

作者： Vegh, Laszlo A. London Sch Econ & Polit Sci Dept Management London England

ISBN: (纸本)9781450327107

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of steps, an arc can be identified that must be tight in every dual optimal solution, and thus can be contracted.

关键词： generalized flows strongly polynomial algorithms linear programming combinatorial algorithms

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Diverse Adaptive Bulk Search: a Framework for Solving QUBO Problems on Multiple GPUs

Diverse Adaptive Bulk Search: a Framework for Solving QUBO P...

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37th IEEE International Parallel and Distributed Processing Symposium (IPDPS)

作者： Nakano, Koji Takafuji, Daisuke Ito, Yasuaki Yazane, Takashi Yano, Junko Ozaki, Shiro Katsuki, Ryota Mori, Rie Hiroshima Univ Grad Sch Adv Sci & Engn Kagamiyama 1-4-1 Higashihiroshima 7398527 Japan NTT DATA Corp Res & Dev Headquarters Toyosu Ctr BldgAnnex3-9Toyosu 3-chomeKoto ku Tokyo 1358671 Japan

ISBN: (纸本)9798350311990

Quadratic Unconstrained Binary Optimization (QUBO) is a combinatorial optimization to find an optimal binary solution vector that minimizes the energy value defined by a quadratic formula of binary variables in the vector. As many NP-hard problems can be reduced to QUBO problems, considerable research has gone into developing QUBO solvers running on various computing platforms such as quantum devices, ASICs, FPGAs, GPUs, and optical fibers. This paper presents a framework called Diverse Adaptive Bulk Search (DABS), which has the potential to find optimal solutions of many types of QUBO problems. Our DABS solver employs a genetic algorithm-based search algorithm featuring three diverse strategies: multiple search algorithms, multiple genetic operations, and multiple solution pools. During the execution of the solver, search algorithms and genetic operations that succeeded in finding good solutions are automatically selected to obtain better solutions. Moreover, search algorithms traverse between different solution pools to find good solutions. We have implemented our DABS solver to run on multiple GPUs. Experimental evaluations using eight NVIDIA A100 GPUs confirm that our DABS solver succeeds in finding optimal or potentially optimal solutions for three types of QUBO problems.

关键词： Quantum annealing combinatorial algorithms heuristic algorithms genetic algorithms GPGPU

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Efficient Synthesis of Mutants Using Genetic Crosses 18

Efficient Synthesis of Mutants Using Genetic Crosses

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9th ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics (ACM-BCB)

作者： Pratapa, Aditya Jalihal, Amogh P. Ravi, S. S. Murali, T. M. Virginia Tech Dept Comp Sci Blacksburg VA 24061 USA Virginia Tech Genet Bioinformat & Computat Biol Blacksburg VA USA Virginia Tech Biocomplex Inst Blacksburg VA USA SUNY Albany Dept Comp Sci Albany NY 12222 USA

ISBN: (纸本)9781450357944

The genetic cross is a fundamental, flexible, and widely-used experimental technique to create new mutant strains from existing ones. Surprisingly, the problem of how to efficiently compute a sequence of crosses that can make a desired target mutant from a set of source mutants has received scarce attention. In this paper, we make three contributions to this question. First, we formulate several natural problems related to efficient synthesis of a target mutant from source mutants. Our formulations capture experimentally-useful notions of verifiability (e.g., the need to confirm that a mutant contains mutations in the desired genes) and permissibility (e.g., the requirement that no intermediate mutants in the synthesis be inviable). Second, we develop combinatorial techniques to solve these problems. We prove that checking the existence of a verifiable, permissible synthesis is NP-complete in general. We complement this result with three polynomial time or fixed-parameter tractable algorithms for optimal synthesis of a target mutant for special cases of the problem that arise in practice. Third, we apply these algorithms to simulated data and to synthetic data. We use results from simulations of a mathematical model of the cell cycle to replicate realistic experimental scenarios where a biologist may be interested in creating several mutants in order to verify model predictions. Our results show that the consideration of permissible mutants can affect the existence of a synthesis or the number of crosses in an optimal one. Our algorithms gracefully handle the restrictions that permissible mutants impose. Results on synthetic data show that our algorithms scale well with increases in the size of the input and the fixed parameters.

关键词： experiment planning genetic crosses multi-gene mutants fixed-parameter tractability combinatorial algorithms mathematical models

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A Generic Algorithmic Framework to Solve Special Versions of the Set Partitioning Problem 26

A Generic Algorithmic Framework to Solve Special Versions of...

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26th IEEE International Conference on Tools with Artificial Intelligence (ICTAI)

作者： Lamarche-Perrin, Robin Demazeau, Yves Vincent, Jean-Marc Max Planck Inst Math Sci Leipzig Germany CNRS Lab Informat Grenoble F-75700 Paris France Univ Grenoble Alpes Lab Informat Grenoble Grenoble France

ISBN: (纸本)9781479965731

Given a set of individuals, a collection of subsets, and a cost associated to each subset, the Set Partitioning Problem (SPP) consists in selecting some of these subsets to build a partition of the individuals that minimizes the total cost. This combinatorial optimization problem has been used to model dozens of problems arising in specific domains of Artificial Intelligence and Operational Research, such as coalition structures generation, community detection, multilevel data analysis, workload balancing, image processing, and database optimization. All these applications are actually interested in special versions of the SPP where assumptions regarding the admissible subsets constraint the search space and allow tractable optimization algorithms. However, there is a major lack of unity regarding the identification, the formalization, and the resolution of these strongly-related problems. This paper hence proposes a generic framework to design dynamic programming algorithms that fit with the particular algebraic structure of special versions of the SPP. We show how this framework can be applied to two well-known versions, thus opening a unified approach to solve new ones that might arise in the future.

关键词： Problem Solving Constraint satisfaction combinatorial algorithms Dynamic programming

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Influence of Professor T. C. Hu's Works on Fundamental Approaches in Layout 18

Influence of Professor T. C. Hu's Works on Fundamental Appro...

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ACM International Symposium on Physical Design (ISPD)

作者： Kahng, Andrew B. UCSD Dept CSE La Jolla CA 92093 USA UCSD Dept ECE La Jolla CA 92093 USA

ISBN: (纸本)9781450356268

Professor T. C. Hu has made numerous pioneering and fundamental contributions in combinatorial algorithms, mathematical programming and operations research. His seminal 1985 IEEE book VLSI Circuit Layout: Theory and Design, coedited with Prof. E. S. Kuh, shaped algorithmic and optimization perspectives, as well as basic frameworks, for IC physical design throughout the following decades [44]. Indeed, Professor Hu gave a keynote address at the very first International Symposium on Physical Design, in April 1997 [41]. His research approach of (i) studying small and/or extremal cases first, (ii) always seeking to establish error bounds or other properties of heuristic outcomes (hence, always seeking to understand optimal solutions), (iii) approaching new problems from as fresh a perspective as possible, and (iv) pursuing simplicity and beauty in both formulation and exposition, has influenced generations of researchers. This paper complements [20] in recounting highlights of Professor Hu's contributions to, and impacts on, physical design. The focus is on several problems of "connection", as well as the concept of "shadow price", as they relate to layout.

关键词： tribute combinatorial algorithms mathematical programming operations research physical design

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If the Current Clique algorithms are Optimal, so is Valiant's Parser 56

If the Current Clique Algorithms are Optimal, so is Valiant'...

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56th IEEE Annual Symposium on Foundations of Computer Science (FOCS)

作者： Abboud, Amir Backurs, Arturs Williams, Virginia Vassilevska Stanford Univ Dept Comp Sci Palo Alto CA 94304 USA MIT EECS Cambridge MA 02139 USA

ISBN: (纸本)9781467381918

The CFG recognition problem is: given a context-free grammar G and a string w of length n, decide if w can be obtained from G. This is the most basic parsing question and is a core computer science problem. Valiant's parser from 1975 solves the problem in O(n(omega)) time, where omega < 2.373 is the matrix multiplication exponent. Dozens of parsing algorithms have been proposed over the years, yet Valiant's upper bound remains unbeaten. The best combinatorial algorithms have mildly subcubic O(n(3)/log(3) n) complexity. Lee (JACM'01) provided evidence that fast matrix multiplication is needed for CFG parsing, and that very efficient and practical algorithms might be hard or even impossible to obtain. Lee showed that any algorithm for a more general parsing problem with running time O(vertical bar G vertical bar center dot n(3-epsilon)) can be converted into a surprising subcubic algorithm for Boolean Matrix Multiplication. Unfortunately, Lee's hardness result required that the grammar size be vertical bar G vertical bar = Omega(n(6)). Nothing was known for the more relevant case of constant size grammars. In this work, we prove that any improvement on Valiant's algorithm, even for constant size grammars, either in terms of runtime or by avoiding the inefficiencies of fast matrix multiplication, would imply a breakthrough algorithm for the k-Clique problem: given a graph on n nodes, decide if there are k that form a clique. Besides classifying the complexity of a fundamental problem, our reduction has led us to similar lower bounds for more modern and well-studied cubic time problems for which faster algorithms are highly desirable in practice: RNA Folding, a central problem in computational biology, and Dyck Language Edit Distance, answering an open question of Saha (FOCS' 14).

关键词： context free grammars parsing CFG recognition clique conditional lower bounds RNA folding Dyck Edit Distance hardness in P tight hardness combinatorial algorithms Valiant's algorithm natural language processing parameterized complexity

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A polynomial time algorithm to compute quantum invariants of 3-manifolds with bounded first Betti number 28

A polynomial time algorithm to compute quantum invariants of...

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28th Annual ACM-SIAM Symposium on Discrete algorithms (SODA)

作者： Maria, Clement Spreer, Jonathan Univ Queensland Brisbane Qld Australia

ISBN: (纸本)9781611974782

In this article, we introduce a fixed parameter tractable algorithm for computing the Turaev-Viro invariants TV4,q, using the dimension of the first homology group of the manifold as parameter. This is, to our knowledge, the first parameterised algorithm in computational 3-manifold topology using a topological parameter. The computation of TV4,q is known to be #P-hard in general;using a topological parameter provides an algorithm polynomial in the size of the input triangulation for the extremely large family of 3-manifolds with first homology group of bounded rank. Our algorithm is easy to implement and running times are comparable with running times to compute integral homology groups for standard libraries of triangulated 3-manifolds. The invariants we can compute this way are powerful: in combination with integral homology and using standard data sets we are able to roughly double the pairs of 3-manifolds we can distinguish. We hope this qualifies TV4,q to be added to the short list of standard properties (such as orientability, connectedness, Betti numbers, etc.) that can be computed ad-hoc when first investigating an unknown triangulation.

关键词： fixed parameter tractable algorithms Turaev-Viro invariants triangulations of 3-manifolds (integral) homology almost normal surfaces combinatorial algorithms

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Minimization of logical function's system by fuzzy clusterization 7

Minimization of logical function's system by fuzzy clusteriz...

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7th International Conference of the Experience of Designing and Application of CAD Systems in Microelectronics

作者： Melnyk, R Lviv Polytech Natl Univ UA-79046 Lvov Ukraine

The minimization approach for the system of logical functions based on fuzzy reduction tree or fuzzy clusterization is considered. The algorithms to form the reduction tree for graphs and covers to obtain minimal logi... 详细信息

ISBN: (纸本)9665532782

关键词： logical functions fuzzy clusterization fuzzy reduction tree combinatorial algorithms

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algorithms FOR STRUCTURAL VARIATION DISCOVERY USING MULTIPLE SEQUENCE SIGNATURES

ALGORITHMS FOR STRUCTURAL VARIATION DISCOVERY USING MULTIPLE...

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作者： Arda Soylev Bilkent University

学位级别：博士

Genomic variations including single nucleotide polymorphisms (SNPs), small INDELs and structural variations (SVs) are known to have significant phenotypic effects on individuals. Among them, SVs, that alter more than 50 nucleotides of DNA, are the major source of complex genetic diseases such as Crohn's, schizophrenia and autism. Additionally, the total number of nucleotides affected by SVs are substantially higher than SNPs (3.5 Mbp SNP, 15-20 Mbp SV). Today, we are able to perform whole genome sequencing (WGS) by utilizing high throughput sequencing technology (HTS) to discover these modifications unimaginably faster, cheaper and more accurate than before. However, as demonstrated in the 1000 Genomes Project, HTS technology still has significant limitations. The major problem lies in the short read lengths (<250 bp) produced by the current sequencing platforms and the fact that most genomes include large amounts of repeats make it very challenging to unambiguously map and accurately characterize genomic variants. Thus, most of the existing SV discovery tools focus on detecting relatively simple types of SVs such as insertions, deletions, and short inversions. In fact, other types of SVs including the complex ones are of crucial importance and several have been associated with genomic disorders. To better understand the contribution of these SVs to human genome, we need new approaches to accurately discover and genotype such variants. Therefore, there is still a need for accurate algorithms to fully characterize a broader spectrum of SVs and thus improve calling accuracy of more simple variants. Here we introduce TARDIS that harbors novel algorithms to accurately characterize various types of SVs including deletions, novel sequence insertions, inversions, transposon insertions, nuclear mitochondria insertions, tandem duplications and interspersed segmental duplications in direct or inverted orientations using short read whole genome sequencing datasets. Within our

关键词： Structural variation high throughput sequencing combinatorial algorithms

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