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Exact and Approximation algorithms for Optimal Equipment Selection in Deploying In-Building Distributed Antenna Systems

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IEEE TRANSACTIONS ON MOBILE COMPUTING 2015年第4期14卷 702-713页

作者： Adjiashvili, David Bosio, Sandro Li, Yuan Yuan, Di ETH Inst Operat Res CH-8092 Zurich Switzerland ETH Dept Math CH-8092 Zurich Switzerland Lund Univ Dept Elect & Informat Technol S-22363 Lund Sweden Linkoping Univ Dept Sci & Technol Norrkoping Sweden

We consider a combinatorial optimization problemin passive In-Building Distributed Antenna Systems (IB-DAS) deployment for indoor mobile broadband service. These systems have a tree topology, in which a central base station is connected to a number of antennas located at tree leaves via cables represented by the tree edges. Each inner node corresponds to a power equipment, of which the available types differ in the number of output ports and/or by power gain at the ports. This paper focuses on the equipment selection problemthat amounts to, for a given passive DAS tree topology, selecting a power equipment type for each inner node and assigning the outgoing edges of the node to the equipment ports. The performance metric is the power deviation at the antennas from the target values. We consider as objective function the minimization of either the total or the largest power deviation over all antennas. Our contributions are the development of exact pseudo-polynomial time algorithms and (additive) fully-polynomial time approximation schemes for both objectives. Numerical results are provided to illustrate the algorithms. We also extend some results to account for equipment cost.

关键词： Wireless communication combinatorial algorithms trees

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An Algorithmic-type Classification of Tetravalent One-regular Graphs Using Computer Algebra Tools

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FUNDAMENTA INFORMATICAE 2014年第3期135卷 211-228页

作者： Ghasemi, Mohsen Urmia Univ Dept Math Orumiyeh 57135 Iran

A finite graph is one-regular if its automorphism group acts regularly on the set of its arcs. In the present paper, tetravalent one-regular graphs of order 7p(2), where p is a prime, are classified using computer alg... 详细信息

关键词： s-transitive graphs symmetric graphs Cayley graphs magma combinatorial algorithms

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The external constraint 4 nonempty part sandwich problem

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DISCRETE APPLIED MATHEMATICS 2011年第7期159卷 661-673页

作者： Teixeira, Rafael B. Dantas, Simone de Figueiredo, Celina M. H. Univ Fed Rural Rio de Janeiro Inst Ciencias Exatas Rio De Janeiro Brazil Univ Fed Fluminense Inst Matemat BR-24220000 Niteroi RJ Brazil Univ Fed Rio de Janeiro COPPE BR-21941 Rio De Janeiro Brazil

List partitions generalize list colourings. Sandwich problems generalize recognition problems. The polynomial dichotomy (NP-complete versus polynomial) of list partition problems is solved for 4-dimensional partitions with the exception of one problem (the LIST STUBBORN PROBLEM) for which the complexity is known to be quasipolynomial. Every partition problem for 4 nonempty parts and only external constraints is known to be polynomial with the exception of one problem (the 2K(2)-PARTITION PROBLEM) for which the complexity of the corresponding list problem is known to be NP-complete. The present paper considers external constraint 4 nonempty part sandwich problems. We extend the tools developed for polynomial solutions of recognition problems obtaining polynomial solutions for most corresponding sandwich versions. We extend the tools developed for NP-complete reductions of sandwich partition problems obtaining the classification into NP-complete for some external constraint 4 nonempty part sandwich problems. On the other hand and additionally, we propose a general strategy for defining polynomial reductions from the 2K(2)-PARTITION PROBLEM to several external constraint 4 nonempty part sandwich problems, defining a class of 2K(2)-hard problems. Finally, we discuss the complexity of the Skew Partition Sandwich Problem. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Graph sandwich problems List partitions Computational complexity combinatorial algorithms Applied combinatorics

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Improving minimum cost spanning trees by upgrading nodes

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JOURNAL OF algorithms 1999年第1期33卷 92-111页

作者： Krumke, SO Marathe, MV Noltemeier, H Ravi, R Ravi, SS Sundarum, R Wirth, HC Univ Wurzburg Dept Comp Sci D-97074 Wurzburg Germany Univ Calif Los Alamos Natl Lab Los Alamos NM 87545 USA Univ Wurzburg Dept Comp Sci D-97074 Wurzburg Germany Carnegie Mellon Univ Grad Sch Ind Adm Pittsburgh PA 15213 USA SUNY Albany Dept Comp Sci Albany NY 12222 USA Delta Global Trading LP Boston MA 02111 USA

We study budget constrained network upgrading problems. We are given an undirected edge-weighted graph G = (V, E), where node upsilon E V can be upgraded at a cost of c(upsilon). This upgrade reduces the weight of each edge incident on upsilon. The goal is to find a minimum cost set of nodes to be upgraded so that the resulting network has a minimum spanning tree of weight no more than a given budget D. The results obtained in the paper include 1. On the positive side, we provide a polynomial time approximation algorithm for the above upgrading problem when the difference between the maximum and minimum edge weights is bounded by a polynomial in n, the number of nodes in the graph. The solution produced by the algorithm satisfies the budget constraint, and the cost of the upgrading set produced by the algorithm is O(log n) times the minimum upgrading cost needed to obtain a spanning tree of weight at most D. 2. In contrast, we show that, unless N-O subset of or equal to DTIME(n(O)((log log n))), there can be no polynomial time approximation algorithm for the problem that produces a solution with upgrading cost at most alpha < In n times the optimal upgrading cost even if the budget can be violated by a factor f(n), for any polynomial time computable function f(rt). This result continues to hold, with f(n) = n(k) being any polynomial, even when the difference between the maximum and minimum edge weights is bounded by a polynomial in n. 3. Finally, we show that using a sample binary search over the set of admissible values, the dual problem can be solved with an appropriate performance guarantee, (C) 1999 Academic Press.

关键词： approximation algorithms bicriteria problems spanning trees network design combinatorial algorithms

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Improving Strand Pairing Prediction through Exploring Folding Cooperativity

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2008年第4期5卷 484-491页

作者： Jeong, Jieun Berman, Piotr Przytycka, Teresa M. Penn State Univ Dept Comp Sci & Engn University Pk PA 16802 USA NIH Computat Biol Branch Natl Ctr Biotechnol Informat Natl Lib Med Bethesda MD 20894 USA

The topology of beta-sheets is defined by the pattern of hydrogen-bonded strand pairing. Therefore, predicting hydrogen-bonded strand partners is a fundamental step toward predicting beta-sheet topology. At the same time, finding the correct partners is very difficult due to long-range interactions involved in strand pairing. Additionally, patterns of amino acids observed in beta-sheet formations are very general, and therefore, difficult to use for computational recognition of specific contacts between strands. In this work, we report a new strand pairing algorithm. To address the aforementioned difficulties, our algorithm attempts to mimic elements of the folding process. Namely, in addition to ensuring that the predicted hydrogen-bonded strand pairs satisfy basic global consistency constraints, it takes into account hypothetical folding pathways. Consistently with this view, introducing hydrogen bonds between a pair of strands changes the probabilities of forming hydrogen bonds between other pairs of strand. We demonstrate that this approach provides an improvement over previously proposed algorithms. We also compare the performance of this method to that of a global optimization algorithm that poses the problem as integer linear programming optimization problem and solves it using ILOG CPLEX package.

关键词： Biology and genetics combinatorial algorithms

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POLYNOMIAL-TIME DATA REDUCTION FOR THE SUBSET INTERCONNECTION DESIGN PROBLEM

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2015年第1期29卷 1-25页

作者： Chen, Jiehua Komusiewicz, Christian Niedermeier, Rolf Sorge, Manuel Suchy, Ondrej Weller, Mathias TU Berlin Inst Softwaretech & Theoret Informat Berlin Germany Czech Tech Univ Dept Theoret Comp Sci CR-16635 Prague Czech Republic Univ Montpellier LIRMM Dept Informat F-34059 Montpellier France

The NP-hard SUBSET INTERCONNECTION DESIGN problem, also known as MINIMUM TOPIC-CONNECTED OVERLAY, is motivated by numerous applications including the design of scalable overlay networks and vacuum systems. It has as input a finite set V and a collection of subsets V-1, V-2, . . ., V-m subset of V, and asks for a minimum-cardinality edge set E such that for the graph G = ( V, E) all induced subgraphs G[V-1], G[V-2], . . ., G[V-m] are connected. We study SUBSET INTERCONNECTION DESIGN in the context of polynomial-time data reduction rules that preserve the possibility of constructing optimal solutions. Our contribution is threefold: First, we show the incorrectness of earlier polynomial-time data reduction rules. Second, we show linear-time solvability in case of a constant number m of subsets, implying fixed-parameter tractability for the parameter m. Third, we provide a fixed-parameter tractability result for small subset sizes and tree-like output graphs. To achieve our results, we elaborate on polynomial-time data reduction rules which also may be of practical use in solving SUBSET INTERCONNECTION DESIGN.

关键词： NP-hard problem fixed-parameter tractability kernelization combinatorial algorithms preprocessing hypergraph support

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Finding the k most vital edges with respect to minimum spanning trees for fixed k

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DISCRETE APPLIED MATHEMATICS 2001年第2-3期113卷 319-327页

作者： Liang, WF Australian Natl Univ Dept Comp Sci Canberra ACT 0200 Australia

Assume that G(V,E) is a weighted, undirected, connected graph with n vertices. The k most vital edge problem with respect to a minimum spanning tree is to find a set S* of k edges from E such that the removal of the edges in S* results in the greatest increase in the weight of the minimum spanning tree in the resulting graph G(V,E-S*). In this paper, an improved algorithm for the problem with fixed k, k greater than or equal to 2, has been presented. The proposed algorithm runs in time O(n(k)alpha((k + 1)(n - 1), n)), which improves a previously known result by an O(n/alpha ((k + 1)(n - 1), n)) factor, where a is a functional inverse of Ackermann's function which grows very slow. The parallel version of the algorithm takes O(log n log log n) time using O(n(k)/log n) processors on a CREW PRAM. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： combinatorial algorithms minimum spanning trees most vital edges network optimization parallel algorithms

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Progressive tree neighborhood applied to the Maximum Parsimony problem

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2008年第1期5卷 136-145页

作者： Goeffon, Adrien Richer, Jean-Michel Hao, Jin-Kao Univ Angers Lab Etude Rech & Informat Angers F-49045 Angers France

The Maximum Parsimony (MP) problem aims at reconstructing a phylogenetic tree from DNA sequences while minimizing the number of genetic transformations. To solve this NP-complete problem, heuristic methods have been developed, often based on local search. In this paper, we focus on the influence of the neighborhood relations. After analyzing the advantages and drawbacks of the well-known Nearest Neighbor Interchange (NNI), Subtree Pruning Regrafting (SPR), and Tree-Bisection-Reconnection (TBR) neighborhoods, we introduce the concept of Progressive Neighborhood (PN), which consists of constraining progressively the size of the neighborhood as the search advances. We empirically show that applied to the MP problem, this PN turns out to be more efficient and robust than the classic neighborhoods using a descent algorithm. Indeed, it allows us to find better solutions with a smaller number of iterations or trees evaluated.

关键词： optimization combinatorial algorithms phylogeny reconstruction Maximum Parsimony

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Optimal resilient sorting and searching in the presence of memory faults

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THEORETICAL COMPUTER SCIENCE 2009年第44期410卷 4457-4470页

作者： Finocchi, Irene Grandoni, Fabrizio Italiano, Giuseppe F. Univ Roma La Sapienza Dipartimento Informat I-00198 Rome Italy Univ Roma Tor Vergata Dipartimento Informat Sistemi & Prod I-00133 Rome Italy

We investigate the problem of reliable computation in the presence of faults that may arbitrarily corrupt memory locations. In this framework, we consider the problems of sorting and searching in optimal time while tolerating the largest possible number of memory faults. In particular, we design an O(n log n) time sorting algorithm that can optimally tolerate up to O(root n log n) memory faults. In the special case of integer sorting, we present an algorithm with linear expected running time that can tolerate O(root n) faults. We also present a randomized searching algorithm that can optimally tolerate up to O(log n) memory faults in O(log n) expected time, and an almost optimal deterministic searching algorithm that can tolerate O((log n)(1-epsilon)) faults, for any small positive constant epsilon, in O(log n) worst-case time. All these results improve over previous bounds. (c) 2009 Elsevier B.V. All rights reserved.

关键词： combinatorial algorithms Sorting Searching Memory faults Memory models Computing with unreliable information

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Sorting and Searching in Faulty Memories

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ALGORITHMICA 2008年第3期52卷 309-332页

作者： Finocchi, Irene Italiano, Giuseppe F. Univ Roma La Sapienza Dipartimento Informat I-00198 Rome Italy Univ Roma Tor Vergata Dipartimento Informat Sistemi & Prod I-00133 Rome Italy

In this paper we investigate the design and analysis of algorithms resilient to memory faults. We focus on algorithms that, despite the corruption of some memory values during their execution, are nevertheless able to produce a correct output at least on the set of uncorrupted values. In this framework, we consider two fundamental problems: sorting and searching. In particular, we prove that any O(n log n) comparison-based sorting algorithm can tolerate the corruption of at most O((n log n)(1/2)) keys. Furthermore, we present one comparison-based sorting algorithm with optimal space and running time that is resilient to O((n log n)(1/3)) memory faults. We also prove polylogarithmic lower and upper bounds on resilient searching.

关键词： combinatorial algorithms Sorting Searching Memory faults Memory models Computing with unreliable information

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