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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第10期70卷 7179-7192页

作者： Bui, Thach V. Scarlett, Jonathan Natl Univ Singapore Dept Comp Sci Singapore 117417 Singapore Natl Univ Singapore Fac Engn Singapore 117575 Singapore Natl Univ Singapore Dept Math Dept Comp Sci Singapore 117417 Singapore Natl Univ Singapore Inst Data Sci Singapore 117417 Singapore

In this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple "types" of items. Specifically, we assume that there are multiple disjoint semi-defective sets, and a test is positive if and only if it contains at least one item from each of these sets. The goal is to reliably identify all of the semi-defective sets using as few tests as possible, and we refer to this problem as Concomitant Group Testing (ConcGT). We derive a variety of algorithms for this task, focusing primarily on the case that there are two semi-defective sets. Our algorithms are distinguished by (i) whether they are deterministic (zero-error) or randomized (small-error), and (ii) whether they are non-adaptive, fully adaptive, or have limited adaptivity (namely, 2 or 3 stages). Both our deterministic adaptive algorithm and our randomized algorithms (non-adaptive or limited adaptivity) are order-optimal in broad scaling regimes of interest, and improve significantly over baseline results that are based on solving a more general problem as an intermediate step (e.g., hypergraph learning).

关键词： Testing Drugs Standards Diseases Decoding Chemicals Upper bound Group testing sparsity discrete algorithms information-theoretic bounds

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Continuous and discrete gradient-Zhang neuronet (GZN) with analyses for time-variant overdetermined linear equation system solving as well as mobile localization applications

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NEUROCOMPUTING 2023年 561卷

作者： Tang, Zanyu Zhang, Yunong Sun Yat Sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Jishou Univ Coll Informat Sci & Engn Jishou 416000 Peoples R China

In this paper, a novel continuous gradient-Zhang neuronet (GZN) model and three discrete GZN algorithms are proposed to solve time-variant overdetermined linear equation system (TVOLES) problems, and are developed on the basis of a gradient neuronet and Zhang neuronet. Specifically, the continuous GZN model is proposed and derived in the form of an explicit-dynamic equation, and its stability is analysed and proven using Lyapunov theory. To ensure that the problems can be solved and implemented on digital platforms, three discrete GZN algorithms are established by using three different discretization formulas. The numerical simulative results verify that, compared with the Zhang neuronet model, gradient neuronet model and variant-parameter neuronet model, the proposed continuous GZN model converges faster in some cases. Other computer experiments further substantiate that the proposed continuous model and its corresponding discrete GZN algorithms are effective and efficient. Finally, the proposed discrete GZN algorithms are applied to mobile object localizations, and the simulative results verify their applicability and effectiveness.

关键词： Gradient-Zhang neuronet Time-variant overdetermined linear equation system discrete algorithms Mobile object localizations

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The generic combinatorial algorithm for image matching with classes of projective transformations

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INFORMATION AND COMPUTATION 2020年 275卷 104550-104550页

作者： Rosenke, Christian Liskiewicz, Maciej Univ Rostock Inst Informat Albert Einstein Str 22 D-18059 Rostock Germany Univ Lubeck Inst Theoret Informat Ratzeburger Allee 160 D-23538 Lubeck Germany

Image matching is an important task arising in video compression, optical character recognition, medical imaging, watermarking and in many others fields. Given two digital images A and B, image matching determines a transformation f for A such that it most closely resembles B. In this paper, we introduce the first general discretization technique that works for the class of projective transformations as well as plenty of its subclasses such as affine transformations and several combinations of scaling, rotation and translation. Based on this, we provide a fully generic image matching algorithm for all these classes that runs in polynomial time. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Digital image matching discrete algorithms Discretization of function spaces Projective transformations Computational geometry

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A Polynomial-Time Algorithm to Compute Turaev-Viro Invariants TV4,q of 3-Manifolds with Bounded First Betti Number

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2020年第5期20卷 1013-1034页

作者： Maria, Clement Spreer, Jonathan INRIA Sophia Antipolis Mediterranee Valbonne France Univ Sydney Sydney NSW 2006 Australia

In this article, we introduce a fixed-parameter tractable algorithm for computing the Turaev-Viro invariants TV4, q, using the first Betti number, i.e. the dimension of the first homology group of the manifold with Z(2)-coefficients, 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 family of 3-manifolds with first Z(2)-homology group of bounded dimension. 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 almost 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 and Betti numbers) 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 (Generalised)normal surfaces discrete algorithms

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On the complexity of the FIFO stack-up problem

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2016年第1期83卷 33-52页

作者： Gurski, Frank Rethmann, Jochen Wanke, Egon Univ Dusseldorf Inst Comp Sci D-40225 Dusseldorf Germany Niederrhein Univ Appl Sci Fac Elect Engn & Comp Sci D-47805 Krefeld Germany

We study the combinatorial FIFO stack-up problem. In delivery industry, bins have to be stacked-up from conveyor belts onto pallets with respect to customer orders. Given k sequences of labeled bins and a positive integer p, the aim is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto an initially empty pallet of unbounded capacity located at one of p stack-up places. Bins with different pallet labels have to be placed on different pallets, bins with the same pallet label have to be placed on the same pallet. After all bins for a pallet have been removed from the given sequences, the corresponding stack-up place will be cleared and becomes available for a further pallet. The FIFO stack-up problem is to find a stack-up sequence such that all pallets can be build-up with the available p stack-up places. In this paper, we introduce two digraph models for the FIFO stack-up problem, namely the processing graph and the sequence graph. We show that there is a processing of some list of sequences with at most p stack-up places if and only if the sequence graph of this list has directed pathwidth at most . This connection implies that the FIFO stack-up problem is NP-complete in general, even if there are at most 6 bins for every pallet and that the problem can be solved in polynomial time, if the number p of stack-up places is assumed to be fixed. Further the processing graph allows us to show that the problem can be solved in polynomial time, if the number k of sequences is assumed to be fixed.

关键词： Computational complexity Combinatorial optimization Directed pathwidth discrete algorithms

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Structure-Based algorithms for Microvessel Classification

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MICROCIRCULATION 2015年第2期22卷 99-108页

作者： Smith, Amy F. Secomb, Timothy W. Pries, Axel R. Smith, Nicolas P. Shipley, Rebecca J. Univ Oxford Math Inst Oxford Ctr Collaborat Appl Math Oxford England Univ Arizona Dept Physiol Tucson AZ USA Charite Dept Physiol D-13353 Berlin Germany Kings Coll London St Thomas Hosp Dept Biomed Engn London WC2R 2LS England Univ Auckland Fac Engn Auckland 1 New Zealand UCL Dept Mech Engn London WC1E 7JE England

ObjectiveRecent developments in high-resolution imaging techniques have enabled digital reconstruction of three-dimensional sections of microvascular networks down to the capillary scale. To better interpret these large data sets, our goal is to distinguish branching trees of arterioles and venules from capillaries. MethodsTwo novel algorithms are presented for classifying vessels in microvascular anatomical data sets without requiring flow information. The algorithms are compared with a classification based on observed flow directions (considered the gold standard), and with an existing resistance-based method that relies only on structural data. ResultsThe first algorithm, developed for networks with one arteriolar and one venular tree, performs well in identifying arterioles and venules and is robust to parameter changes, but incorrectly labels a significant number of capillaries as arterioles or venules. The second algorithm, developed for networks with multiple inlets and outlets, correctly identifies more arterioles and venules, but is more sensitive to parameter changes. ConclusionsThe algorithms presented here can be used to classify microvessels in large microvascular data sets lacking flow information. This provides a basis for analyzing the distinct geometrical properties and modelling the functional behavior of arterioles, capillaries, and venules.

关键词： vessel classification discrete algorithms microvascular networks

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In-Flight Identification of Magnetometer and Attitude Determination System for Land-survey Mini-satellite

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IFAC-PapersOnLine 2015年第11 11期48卷 16-21页

作者： Somov, Yevgeny Butyrin, Sergey Hajiyev, Chingiz Samara State Technical University 244 Molodogvardeyskaya Str. Samara443100 Russia Istanbul Technical University Maslak Istanbul34469 Turkey

We present discrete algorithms for in-flight identification, calibration and alignment of a low cost strap-down inertial navigation system with correction by signals from the Sun and magnetic sensors. Proposed algorit... 详细信息

关键词： Satellites Calibration Identification (control systems) Inertial navigation systems Surveys Attitude determination Attitude determination systems Attitude dynamics discrete algorithms Land surveys Low costs Mini satellites Strap down inertial navigation systems

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Casting an Object with a Core

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ALGORITHMICA 2009年第1期54卷 72-88页

作者： Ahn, Hee-Kap Bae, Sang Won Cheng, Siu-Wing Chwa, Kyung-Yong POSTECH Dept Comp Sci & Engn Pohang South Korea Korea Adv Inst Sci & Technol Div Comp Sci Taejon 305701 South Korea HKUST Dept Comp Sci & Engn Pohang Hong Kong Peoples R China

This paper addresses geometric problems in manufacturing objects by casting. In casting, molten material is poured into the cavity of the cast and allowed to solidify, after which the cast is removed. The cast has two cast parts to be removed in opposite directions. To manufacture more complicated objects, the cast may also have a side core to be removed in a direction skewed to the removal directions for the cast parts. We address the following problem: Given an object and the removal directions for the cast parts and the side core, can a cast be constructed such that the cast parts and the side core can be removed in the directions specified without colliding with the object or each other? We give necessary and sufficient conditions for the problem, as well as a discrete algorithm to perform the test in O(n(3) log n) time for polyhedral objects, where n is the number of vertices, edges, and facets. If the test result is positive, a cast with complexity O(n(3)) can be constructed within the same time bound. We also present an example to show that a cast may have Omega(n(3)) complexity in the worst case.

关键词： Manufacturing Casting Core discrete algorithms

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A combinatorial geometrical approach to two-dimensional robust pattern matching with scaling and rotation

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THEORETICAL COMPUTER SCIENCE 2009年第51期410卷 5317-5333页

作者： Hundt, Christian Liskiewicz, Maciej Nevries, Ragnar Univ Rostock Inst Informat D-2500 Rostock 1 Germany Univ Lubeck Inst Theoret Informat Lubeck Germany

The problem of two-dimensional pattern matching invariant under a given class of admissible transformations F is to find matches of transformed versions f (P) of a pattern P in a given text T, for all f in F. In this paper, pattern matching invariant under compositions of real valued scaling and rotation are investigated. We give a new discretization technique for this class of transformations and prove sharp lower and upper bounds on the number of different possibilities to transform a pattern in this way. Subsequently, we present the first efficient pattern matching algorithm invariant under compositions of scaling and rotation. The algorithm works in time O(m(2) n(6)) for patterns of size m(2) and texts of size n(2). We conclude with an experimental section to support the practical use of our results. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Combinatorial pattern matching Digital image matching discrete rotations and scalings discrete algorithms

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Decentralized redistribution for cooperative patrol

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2008年第2期18卷 165-195页

作者： Moore, Brandon J. Passino, Kevin M. Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

This paper addresses the problem of enabling a group of autonomous vehicles to effectively patrol an environment significantly larger than their communication and sensing radii. Our formulation uses an a priori spatial decomposition of the environment into smaller areas in order to provide a framework for the allocation of vehicles to different parts of the environment. We develop a distributed cooperative control algorithm that transfers vehicles between these areas based on only local information and prove that it achieves the proper environment-wide distribution of vehicles within a finite time interval. Various applications are discussed and simulations are included to illustrate convergence dynamics as well as to quantify practical performance as a function of problem parameters. Copyright (c) 2007 John Wiley & Sons, Ltd.

关键词： cooperative control resource balancing discrete algorithms

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