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Information-Theoretic Thresholds for Planted Dense Cycles

IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第2期71卷 1266-1282页

作者： Mao, Cheng Wein, Alexander S. Zhang, Shenduo Georgia Inst Technol Sch Math Atlanta GA 30332 USA Univ Calif Davis Dept Math Davis CA 95616 USA

We study a random graph model for small-world networks which are ubiquitous in social and biological sciences. In this model, a dense cycle of expected bandwidth n tau , representing the hidden one-dimensional geometry of vertices, is planted in an ambient random graph on n vertices. For both detection and recovery of the planted dense cycle, we characterize the information-theoretic thresholds in terms of n, tau , and an edge-wise signal-to-noise ratio lambda . In particular, the information-theoretic thresholds differ from the computational thresholds established in a recent work for low-degree polynomial algorithms, thereby justifying the existence of statistical-to-computational gaps for this problem.

关键词： Information theory Image edge detection Polynomials Biological system modeling Bandwidth Computational efficiency Signal to noise ratio Geometry Prediction algorithms Lower bound Random graphs network theory graphs and networks information theory statistics geometrical problems and computations computations on discrete structures

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Low distortion embeddings for edit distance

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JOURNAL OF THE ACM 2007年第5期54卷 23-1-23-16页

作者： Ostrovsky, Rafail Rabani, Yuval Univ Calif Los Angeles Dept Comp Sci Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel

We show that (0, 1)(d) endowed with edit distance embeds into B, with distortion 2(0)(root log d log d). We further show efficient implementation of the embedding that yield solutions to various computational problems involving edit distance. These include sketching, communication complexity, nearest neighbor search. For all these problems, we improve upon previous bounds.

关键词： algorithms theory pattern matching computations on discrete structures edit distance Levenshtein distance metric embeddings dimension reduction sketching communication complexity nearest neighbor search

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SCJ: A Breakpoint-Like Distance that Simplifies Several Rearrangement Problems

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2011年第5期8卷 1318-1329页

作者： Feijao, Pedro Meidanis, Joao Univ Estadual Campinas Inst Comp Campinas SP Brazil Scylla Bioinformat Campinas SP Brazil

The breakpoint distance is one of the most straightforward genome comparison measures. Surprisingly, when it comes to defining it precisely for multichromosomal genomes with both linear and circular chromosomes, there is more than one way to go about it. Pevzner and Tesler gave a definition in a 2003 paper, Tannier et al. defined it differently in 2008, and in this paper we provide yet another alternative, calling it SCJ for single-cut-or-join, in analogy to the popular double cut and join (DCJ) measure. We show that several genome rearrangement problems, such as median and halving, become easy for SCJ, and provide linear and higher polynomial time algorithms for them. For the multichromosomal linear genome median problem, this is the first polynomial time algorithm described, since for other distances this problem is NP-hard. In addition, we show that small parsimony under SCJ is also easy, and can be solved by a variant of Fitch's algorithm. In contrast, big parsimony is NP-hard under SCJ. This new distance measure may be of value as a speedily computable, first approximation to distances based on more realistic rearrangement models.

关键词： Biology and genetics combinatorial algorithms computations on discrete structures

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Linear Algorithms in Sublinear Time-a Tutorial on Statistical Estimation

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IEEE COMPUTER GRAPHICS AND APPLICATIONS 2011年第2期31卷 58-66页

作者： Ullrich, Torsten Fellner, Dieter W. Fraunhofer Austria Res Vienna Austria

This tutorial presents probability theory techniques for boosting linear algorithms. The approach is based on statistics and uses educated guesses instead of comprehensive calculations. Because estimates can be calcul... 详细信息

关键词： computations on discrete structures computer graphics geometrical problems and computations graphics and multimedia statistical computing COMPUTER GRAPHICS sublinear algorithms image processing algorithm Statistical Computing

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Coalescent-Based Method for Learning Parameters of Admixture Events from Large-Scale Genetic Variation Data

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2013年第5期10卷 1137-1149页

作者： Tsai, Ming-Chi Blelloch, Guy Ravi, R. Schwartz, Russell Joint CMU Pitt PhD Program Computat Biol Pittsburgh PA 15213 USA Carnegie Mellon Univ Dept Comp Sci Pittsburgh PA 15213 USA Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA Carnegie Mellon Univ Dept Biol Sci Pittsburgh PA 15213 USA

Detecting and quantifying the timing and the genetic contributions of parental populations to a hybrid population is an important but challenging problem in reconstructing evolutionary histories from genetic variation data. With the advent of high throughput genotyping technologies, new methods suitable for large-scale data are especially needed. Furthermore, existing methods typically assume the assignment of individuals into subpopulations is known, when that itself is a difficult problem often unresolved for real data. Here, we propose a novel method that combines prior work for inferring nonreticulate population structures with an MCMC scheme for sampling over admixture scenarios to both identify population assignments and learn divergence times and admixture proportions for those populations using genome-scale admixed genetic variation data. We validated our method using coalescent simulations and a collection of real bovine and human variation data. On simulated sequences, our methods show better accuracy and faster runtime than leading competitive methods in estimating admixture fractions and divergence times. Analysis on the real data further shows our methods to be effective at matching our best current knowledge about the relevant populations.

关键词： Biology and genetics graphs and networks information theory computations on discrete structures

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Integer programming approaches to haplotype inference by pure parsimony

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2006年第2期3卷 141-154页

作者： Brown, DG Harrower, IM Univ Waterloo David R Cheriton Sch Comp Sci Waterloo ON N2L 3G1 Canada

In 2003, Gusfield introduced the Haplotype Inference by Pure Parsimony (HIPP) problem and presented an integer program (IP) that quickly solved many simulated instances of the problem [1]. Although it solved well on small instances, Gusfield's IP can be of exponential size in the worst case. Several authors [2], [3] have presented polynomial-sized IPs for the problem. In this paper, we further the work on IP approaches to HIPP. We extend the existing polynomial-sized IPs by introducing several classes of valid cuts for the IP. We also present a new polynomial-sized IP formulation that is a hybrid between two existing IP formulations and inherits many of the strengths of both. Many problems that are too complex for the exponential-sized formulations can still be solved in our new formulation in a reasonable amount of time. We provide a detailed empirical comparison of these IP formulations on both simulated and real genotype sequences. Our formulation can also be extended in a variety of ways to allow errors in the input or model the structure of the population under consideration.

关键词： computations on discrete structures integer programming biology and genetics haplotype inference

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Mandatory Critical Points of 2D Uncertain Scalar Fields

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COMPUTER GRAPHICS FORUM 2014年第3期33卷 31-40页

作者： Guenther, David Salmon, Joseph Tierny, Julien Telecom ParisTech Inst Mines Telecom CNRS LTCI Paris France Telecom ParisTech CNRS LTCI Paris France

This paper introduces a novel, non-local characterization of critical points and their global relation in 2D uncertain scalar fields. The characterization is based on the analysis of the support of the probability density functions (PDF) of the input data. Given two scalar fields representing reliable estimations of the bounds of this support, our strategy identifies mandatory critical points: spatial regions and function ranges where critical points have to occur in any realization of the input. The algorithm provides a global pairing scheme for mandatory critical points which is used to construct mandatory join and split trees. These trees enable a visual exploration of the common topological structure of all possible realizations of the uncertain data. To allow multi-scale visualization, we introduce a simplification scheme for mandatory critical point pairs revealing the most dominant features. Our technique is purely combinatorial and handles parametric distribution models and ensemble data. It does not depend on any computational parameter and does not suffer from numerical inaccuracy or global inconsistency. The algorithm exploits ideas of the established join/split tree computation. It is therefore simple to implement, and its complexity is output-sensitive. We illustrate, evaluate, and verify our method on synthetic and real-world data.

关键词： Categories and Subject Descriptors (according to ACM CCS) F.2.2 [Analysis Of Algorithms And Problem Complexity]: Nonnumerical Algorithms and Problems&mdash computations on discrete structures

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Rank aggregation: New bounds for MCx

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discrete APPLIED MATHEMATICS 2019年 252卷 28-36页

作者： Freund, Daniel Williamson, David P. Cornell Univ Ctr Appl Math Ithaca NY 14853 USA Cornell Univ Sch Operat Res & Informat Engn Ithaca NY USA

The rank aggregation problem has received significant recent attention within the computer science community. Its applications today range far beyond the original aim of building metasearch engines to problems in machine learning, recommendation systems and more. Several algorithms have been proposed for these problems, and in many cases approximation guarantees have been proven for them. However, it is also known that some Markov chain based algorithms (MC1, MC2, MC3, MC4) perform extremely well in practice, yet had no known performance guarantees. We prove supra-constant lower bounds on approximation guarantees for all of them. Nevertheless, we show that in particular ways, MC4 can be seen as a generalization of Copeland score. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Rank aggregation computations on discrete structures Combinatorial algorithms Approximation guarantees

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Counting and sampling SCJ small parsimony solutions

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THEORETICAL COMPUTER SCIENCE 2014年第0期552卷 83-98页

作者： Miklos, Istvan Kiss, Sandor Z. Tannier, Eric Renyi Inst Dept Stochast H-1053 Budapest Hungary Hungarian Acad Sci Inst Comp & Automat Data Min & Search Res Grp H-1111 Budapest Hungary Univ Technol & Econ Dept Algebra H-1111 Budapest Hungary Univ Lyon 1 INRIA Rhone Alpes CNRS Lab Biometrie & Biol EvolutUMR5558 F-69622 Villeurbanne France

The Single Cut or Join (SCJ) operation on genomes, generalizing chromosome evolution by fusions and fissions, is the computationally simplest known model of genome rearrangement. While most genome rearrangement problems are already hard when comparing three genomes, it is possible to compute in polynomial time a most parsimonious SCJ scenario for an arbitrary number of genomes related by a binary phylogenetic tree. Here we consider the problems of sampling and counting the most parsimonious SCJ scenarios. We show that both the sampling and counting problems are easy for two genomes, and we relate SCJ scenarios to alternating permutations. However, for an arbitrary number of genomes related by a binary phylogenetic tree, the counting and sampling problems become hard. We prove that if a Fully Polynomial Randomized Approximation Scheme or a Fully Polynomial Almost Uniform Sampler exist for the most parsimonious SCJ scenario, then RP = NP. The proof has a wider scope than genome rearrangements: the same result holds for parsimonious evolutionary scenarios on any set of discrete characters. (C) 2014 Elsevier B.V. All rights reserved.

关键词： computations on discrete structures Counting problems Single cut and join FPAUS FPRAS Non-approximability

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GPU Computing for Atmospheric Modeling Experience with a Small Kernel and Implications for a Full Model

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COMPUTING IN SCIENCE & ENGINEERING 2010年第4期12卷 26-32页

作者： Kelly, Rory Natl Ctr Atmospher Res Computat & Informat Syst Lab Boulder CO 80307 USA

Much success has been achieved using GPUs to accelerate existing applications that are highly data parallel, or that are dominated by small, intense computational kernels. What are the prospects for porting existing large scientific models that do not fit this mold? We take an expensive routine from the CAM atmosphere model, and port it to a GPU using CUDA. We use the experience gained as a guide in thinking about porting the full application to an accelerator based system. We consider the best path forward for getting large scientific models running on accelerator based systems, and identify cases where porting may be feasible, and where a complete redesign may be the best option.

关键词： computations on discrete structures emerging technologies graphics processors threads

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