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Mathematics and Statistics	50%

Selected Abstracts

Multiversion concurrency control for the generalized search tree

CONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 12 2009
Walter Binder
Abstract Many read-intensive systems where fast access to data is more important than the rate at which data can change make use of multidimensional index structures, like the generalized search tree (GiST). Although in these systems the indexed data are rarely updated and read access is highly concurrent, the existing concurrency control mechanisms for multidimensional index structures are based on locking techniques, which cause significant overhead. In this article we present the multiversion-GiST (MVGiST), an in-memory mechanism that extends the GiST with multiversion concurrency control. The MVGiST enables lock-free read access and ensures a consistent view of the index structure throughout a reader's series of queries, by creating lightweight, read-only versions of the GiST that share unchanging nodes among themselves. An example of a system with high read to write ratio, where providing wait-free queries is of utmost importance, is a large-scale directory that indexes web services according to their input and output parameters. A performance evaluation shows that for low update rates, the MVGiST significantly improves scalability w.r.t. the number of concurrent read accesses when compared with a traditional, locking-based concurrency control mechanism. We propose a technique to control memory consumption and confirm through our evaluation that the MVGiST efficiently manages memory. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Adaptive beam search lookahead algorithms for the circular packing problem

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2010
Hakim Akeb
Abstract This paper addresses the circular packing problem (CPP), which consists in packing n circles Ci, each of known radius ri, i,N={1, ,, n}, into the smallest containing circle C. The objective is to determine the radius r of C as well as the coordinates (xi, yi) of the center of Ci, i,N. CPP is solved using two adaptive algorithms that adopt a binary search to determine r, and a beam search to check the feasibility of packing n circles into C when the radius is fixed at r. A node of level ,, ,=1, ,, n, of the beam search tree corresponds to a partial packing of , circles of N into C. The potential of each node of the tree is assessed using a lookahead strategy that, starting with the partial packing of the current node, assigns each unpacked circle to its maximum hole degree position. The beam search stops either when the lookahead strategy identifies a feasible packing or when it has fathomed all nodes. The computational tests on a set of benchmark instances show the effectiveness of the proposed adaptive algorithms. [source]

Rotamer optimization for protein design through MAP estimation and problem-size reduction

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 12 2009
Eun-Jong Hong
Abstract The search for the global minimum energy conformation (GMEC) of protein side chains is an important computational challenge in protein structure prediction and design. Using rotamer models, the problem is formulated as a NP-hard optimization problem. Dead-end elimination (DEE) methods combined with systematic A* search (DEE/A*) has proven useful, but may not be strong enough as we attempt to solve protein design problems where a large number of similar rotamers is eligible and the network of interactions between residues is dense. In this work, we present an exact solution method, named BroMAP (branch-and-bound rotamer optimization using MAP estimation), for such protein design problems. The design goal of BroMAP is to be able to expand smaller search trees than conventional branch-and-bound methods while performing only a moderate amount of computation in each node, thereby reducing the total running time. To achieve that, BroMAP attempts reduction of the problem size within each node through DEE and elimination by lower bounds from approximate maximum-a-posteriori (MAP) estimation. The lower bounds are also exploited in branching and subproblem selection for fast discovery of strong upper bounds. Our computational results show that BroMAP tends to be faster than DEE/A* for large protein design cases. BroMAP also solved cases that were not solved by DEE/A* within the maximum allowed time, and did not incur significant disadvantage for cases where DEE/A* performed well. Therefore, BroMAP is particularly applicable to large protein design problems where DEE/A* struggles and can also substitute for DEE/A* in general GMEC search. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009 [source]

On the shape of the fringe of various types of random trees

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2009
Michael Drmota
Abstract We analyze a fringe tree parameter w in a variety of settings, utilizing a variety of methods from the analysis of algorithms and data structures. Given a tree t and one of its leaves a, the w(t,,a) parameter denotes the number of internal nodes in the subtree rooted at a's father. The closely related w,(t,,a) parameter denotes the number of leaves, excluding a, in the subtree rooted at a's father. We define the cumulative w parameter as W(t) = ,aw(t,,a), i.e. as the sum of w(t,,a) over all leaves a of t. The w parameter not only plays an important rôle in the analysis of the Lempel,Ziv '77 data compression algorithm, but it is captivating from a combinatorial viewpoint too. In this report, we determine the asymptotic behavior of the w and W parameters on a variety of types of trees. In particular, we analyze simply generated trees, recursive trees, binary search trees, digital search trees, tries and Patricia tries. The final section of this report briefly summarizes and improves the previously known results about the w, parameter's behavior on tries and suffix trees, originally published in one author's thesis (see Analysis of the multiplicity matching parameter in suffix trees. Ph.D. Thesis, Purdue University, West Lafayette, IN, U.S.A., May 2005; Discrete Math. Theoret. Comput. Sci. 2005; AD:307,322; IEEE Trans. Inform. Theory 2007; 53:1799,1813). This survey of new results about the w parameter is very instructive since a variety of different combinatorial methods are used in tandem to carry out the analysis. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs,

RANDOM STRUCTURES AND ALGORITHMS, Issue 4 2007
Surender Baswana
Abstract Let G = (V,E) be an undirected weighted graph on |V | = n vertices and |E| = m edges. A t -spanner of the graph G, for any t , 1, is a subgraph (V,ES), ES , E, such that the distance between any pair of vertices in the subgraph is at most t times the distance between them in the graph G. Computing a t -spanner of minimum size (number of edges) has been a widely studied and well-motivated problem in computer science. In this paper we present the first linear time randomized algorithm that computes a t -spanner of a given weighted graph. Moreover, the size of the t -spanner computed essentially matches the worst case lower bound implied by a 43-year old girth lower bound conjecture made independently by Erd,s, Bollobás, and Bondy & Simonovits. Our algorithm uses a novel clustering approach that avoids any distance computation altogether. This feature is somewhat surprising since all the previously existing algorithms employ computation of some sort of local or global distance information, which involves growing either breadth first search trees up to ,(t)-levels or full shortest path trees on a large fraction of vertices. The truly local approach of our algorithm also leads to equally simple and efficient algorithms for computing spanners in other important computational environments like distributed, parallel, and external memory. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 [source]

Martingales and large deviations for binary search trees

RANDOM STRUCTURES AND ALGORITHMS, Issue 2 2001
Jean Jabbour-Hattab
Abstract We establish an almost sure large deviations theorem for the depth of the external nodes of binary search trees (BSTs). To achieve this, a parametric family of martingales is introduced. This family also allows us to get asymptotic results on the number of external nodes at deepest level. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19: 112,127, 2001 [source]