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57
Cuckoo hashing
 JOURNAL OF ALGORITHMS
, 2001
"... We present a simple dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738–761, 1994). The space usage is similar to that ..."
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Cited by 199 (7 self)
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We present a simple dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738–761, 1994). The space usage is similar to that of binary search trees, i.e., three words per key on average. Besides being conceptually much simpler than previous dynamic dictionaries with worst case constant lookup time, our data structure is interesting in that it does not use perfect hashing, but rather a variant of open addressing where keys can be moved back in their probe sequences. An implementation inspired by our algorithm, but using weaker hash functions, is found to be quite practical. It is competitive with the best known dictionaries having an average case (but no nontrivial worst case) guarantee.
On the design of CGAL a computational geometry algorithms library
 SOFTW. – PRACT. EXP
, 1999
"... CGAL is a Computational Geometry Algorithms Library written in C++, which is being developed by research groups in Europe and Israel. The goal is to make the large body of geometric algorithms developed in the field of computational geometry available for industrial application. We discuss the major ..."
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Cited by 106 (15 self)
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CGAL is a Computational Geometry Algorithms Library written in C++, which is being developed by research groups in Europe and Israel. The goal is to make the large body of geometric algorithms developed in the field of computational geometry available for industrial application. We discuss the major design goals for CGAL, which are correctness, flexibility, easeofuse, efficiency, and robustness, and present our approach to reach these goals. Generic programming using templates in C++ plays a central role in the architecture of CGAL. We give a short introduction to generic programming in C++, compare it to the objectoriented programming paradigm, and present examples where both paradigms are used effectively in CGAL. Moreover, we give an overview of the current structure of the CGALlibrary and consider software engineering aspects in the CGALproject.
Geometric SpeedUp Techniques for Finding Shortest Paths in Large Sparse Graphs
, 2003
"... In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. ..."
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Cited by 58 (15 self)
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In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We assume that a layout of the graph is given. From this layout, in the preprocessing, we determine for each edge a geometric object containing all nodes that can be reached on a shortest path starting with that edge. Based on these geometric objects, the search space for online computation can be reduced significantly. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are traffic networks, the typical field of application for this scenario.
An Algorithm for Clustering cDNAs for Gene Expression Analysis
 In RECOMB99: Proceedings of the Third Annual International Conference on Computational Molecular Biology
, 1999
"... We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques. A similarity graph is defined and clusters in that graph correspond to highly connected subgraphs. A polynomial algorithm to compute them efficiently is presented. Our algorithm produces a clusterin ..."
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Cited by 52 (4 self)
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We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques. A similarity graph is defined and clusters in that graph correspond to highly connected subgraphs. A polynomial algorithm to compute them efficiently is presented. Our algorithm produces a clustering with some provably good properties. The application that motivated this study was gene expression analysis, where a collection of cDNAs must be clustered based on their oligonucleotide fingerprints. The algorithm has been tested intensively on simulated libraries and was shown to outperform extant methods. It demonstrated robustness to high noise levels. In a blind test on real cDNA fingerprint data the algorithm obtained very good results. Utilizing the results of the algorithm would have saved over 70% of the cDNA sequencing cost on that data set. 1 Introduction Cluster analysis seeks grouping of data elements into subsets, so that elements in the same subset are in some sense more cl...
A BranchandCut Algorithm for Multiple Sequence Alignment
 IN PROC. OF THE 1ST ANN. INTERN. CONF. ON COMP. MOLEC. BIO. (RECOMB 97
, 1997
"... Multiple sequence alignment is an important problem in computational biology. We study the Maximum Trace formulation introduced by Kececioglu [Kec91]. We first phrase the problem in terms of forbidden subgraphs, which enables us to express Maximum Trace as an integer linearprogramming problem, and ..."
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Cited by 35 (7 self)
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Multiple sequence alignment is an important problem in computational biology. We study the Maximum Trace formulation introduced by Kececioglu [Kec91]. We first phrase the problem in terms of forbidden subgraphs, which enables us to express Maximum Trace as an integer linearprogramming problem, and then solve the integer linear program using methods from polyhedral combinatorics. The trace polytope is the convex hull of all feasible solutions to the Maximum Trace problem; for the case of two sequences, we give a complete characterization of this polytope. This yields a polynomialtime algorithm for a general version of pairwise sequence alignment that, perhaps suprisingly, does not use dynamic programming; this yields, for instance, a nondynamic programming algorithm for sequence comparison under the 01 metric, which gives another answer to a longopen question in the area of string algorithms [PW93]. For the multiplesequence case, we derive several classes of facetdefining inequali...
Managing Uncertainty in Schema Matching with TopK Schema Mappings
 Journal on Data Semantics
, 2006
"... In this paper, we propose to extend current practice in schema matching with the simultaneous use of topK schema mappings rather than a single best mapping. This is a natural extension of existing methods (which can be considered to fall into the top1 category), taking into account the imprecision ..."
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Cited by 34 (7 self)
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In this paper, we propose to extend current practice in schema matching with the simultaneous use of topK schema mappings rather than a single best mapping. This is a natural extension of existing methods (which can be considered to fall into the top1 category), taking into account the imprecision inherent in the schema matching process. The essence of this method is the simultaneous generation and examination of K best schema mappings to identify useful mappings. The paper discusses efficient methods for generating topK methods and propose a generic methodology for the simultaneous utilization of topK mappings. We also propose a concrete heuristic that aims at improving precision at the cost of recall. We have tested the heuristic on real as well as synthetic data and anlyze the emricial results. The novelty of this paper lies in the robust extension of existing methods for schema matching, one that can gracefully accommodate lessthanperfect scenarios in which the exact mapping cannot be identified in a single iteration. Our proposal represents a step forward in achieving fully automated schema matching, which is currently semiautomated at best. 1
Experimental Analysis of Dynamic Algorithms for the Single Source Shortest Path Problem
 ACM Jounal of Experimental Algorithmics
, 1997
"... In this paper we propose the first experimental study of the fully dynamic single source shortest paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bound ..."
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Cited by 27 (3 self)
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In this paper we propose the first experimental study of the fully dynamic single source shortest paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bounded algorithms proposed by Ramalingam and Reps in [31] and by Frigioni, MarchettiSpaccamela and Nanni in [18], respectively. The main goal of this paper is to provide a first experimental evidence for: (a) the effectiveness of dynamic algorithms for shortest paths with respect to a traditional static approach to this problem; (b) the validity of the theoretical model of output boundedness to analyze dynamic graph algorithms. Beside random generated graphs, useful to capture the "asymptotic" behavior of algorithms, we also develope experiments by considering a widely used graph from the real world, i.e., the Internet graph. Work partially supported by the ESPRIT Long Term Research Project...
Graph Based Modeling and Implementation with EER/GRAL
, 1996
"... This paper gives a cohesive approach to modeling and implementation with graphs. This approach uses extended entity relationship (EER) diagrams supplemented with the Zlike constraint language GRAL. Due to the foundation of EER/GRAL on Z a common formal basis exists. EER/GRAL descriptions give con ..."
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Cited by 25 (14 self)
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This paper gives a cohesive approach to modeling and implementation with graphs. This approach uses extended entity relationship (EER) diagrams supplemented with the Zlike constraint language GRAL. Due to the foundation of EER/GRAL on Z a common formal basis exists. EER/GRAL descriptions give conceptual models which can be implemented in a seamless manner by efficient data structures using the GraLab graph library. Descriptions of four medium size EER/GRALapplications conclude the paper to demonstrate the usefulness of the approach in practice.
An Exact Solution for the SegmenttoSegment Multiple Sequence Alignment Problem
"... In molecular biology sequence alignment is a crucial tool in studying structure and function of molecules as well as evolution of species. In the segmenttosegment variation of the multiple alignment problem the input can be seen as a set of runs of nongapped matches (diagonals) between pairs o ..."
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Cited by 25 (10 self)
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In molecular biology sequence alignment is a crucial tool in studying structure and function of molecules as well as evolution of species. In the segmenttosegment variation of the multiple alignment problem the input can be seen as a set of runs of nongapped matches (diagonals) between pairs of sequences. Given a weight function that assigns a weight score to every possible diagonal, the goal is to choose a consistent set of diagonals of maximum weight. We show that the segmenttosegment multiple alignment problem is equivalent to a novel formulation of the Maximum Weight Trace (MWT) problem. Solving the generalized MWT (GMWT) problem to optimality therefore improves upon the previous greedy strategies that are used for solving the segmenttosegment multiple sequence alignment problem. We show that the GMWT can be stated in terms of an integer linear program and then solve the integer linear program using methods from polyhedral combinatorics. This leads to a branchand...
A polyhedral approach to sequence alignment problems
 DISCRETE APPL. MATH
, 2000
"... We study two new problems in sequence alignment both from a practical and a theoretical view, using tools from combinatorial optimization to develop branchandcut algorithms. The Generalized Maximum Trace formulation captures several forms of multiple sequence alignment problems in a common framewo ..."
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Cited by 24 (2 self)
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We study two new problems in sequence alignment both from a practical and a theoretical view, using tools from combinatorial optimization to develop branchandcut algorithms. The Generalized Maximum Trace formulation captures several forms of multiple sequence alignment problems in a common framework, among them the original formulation of Maximum Trace. The RNA Sequence Alignment Problem captures the comparison of RNA molecules on the basis of their primary sequence and their secondary structure. Both problems have a characterization in terms of graphs which we reformulate in terms of integer linear programming. We then study the polytopes (or convex hulls of all feasible solutions) associated with the integer linear program for both problems. For each polytope we derive several classes of facetdefining inequalities and show that for some of these classes the corresponding separation problem can be solved in polynomial time. This leads to a polynomial time algorithm for pairwise sequence alignment that is not based on dynamic programming. Moreover, for multiple sequences the branchandcut algorithms for both sequence alignment problems are able to solve to optimality instances that are beyond the range of present dynamic programming approaches.