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47
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 bounded al ..."
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Cited by 19 (2 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...
The Practical Use of the A* Algorithm for Exact Multiple Sequence Alignment
 Journal of Computational Biology
, 1997
"... Multiple alignment is an important problem in computational biology. It is well known that it can be solved exactly by a dynamic programming algorithm which in turn can be interpreted as a shortest path computation in a directed acyclic graph. The A algorithm (or goal directed unidirectional search ..."
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Cited by 18 (3 self)
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Multiple alignment is an important problem in computational biology. It is well known that it can be solved exactly by a dynamic programming algorithm which in turn can be interpreted as a shortest path computation in a directed acyclic graph. The A algorithm (or goal directed unidirectional search) is a technique that speeds up the computation of a shortest path by transforming the edge lengths without losing the optimality of the shortest path. We implemented the A algorithm in a computer program similar to MSA [GKS95] and FMA [SI97b]. We incorporated in this program new bounding strategies for both, lower and upper bounds and show that the A algorithm, together with our improvements, can speed up computations considerably. Additionally we show that the A algorithm together with a standard bounding technique is superior to the well known CarilloLipman bounding since it excludes more nodes from consideration. 1 Introduction One of the most prominent problems in computational mo...
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 17 (8 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...
Optimal Labelling of Point Features in Rectangular Labelling Models
 Mathematical Programming
, 2003
"... We investigate the label number maximisation problem (lnm): Given a set of labels , each of which belongs to a point feature in the plane, the task is to nd a largest subset P of so that each 2 P labels the corresponding point feature and no two labels from P overlap. Our approach is based on ..."
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Cited by 13 (2 self)
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We investigate the label number maximisation problem (lnm): Given a set of labels , each of which belongs to a point feature in the plane, the task is to nd a largest subset P of so that each 2 P labels the corresponding point feature and no two labels from P overlap. Our approach is based on two socalled constraint graphs which code horizontal and vertical positioning relations. The key idea is to link the two graphs by a set of additional constraints, thus characterising all feasible solutions of lnm. This enables us to formulate a zeroone integer linear program whose solution leads to an optimal labelling. We can express lnm in both the discrete and the slider labelling models. The slider models allow a continuous movement of a label around its point feature, leading to a signicantly higher number of labels that can be placed. To our knowledge, we present the rst algorithm that computes provably optimal solutions in the slider models. We nd it remarkable that our approach is independent of the labelling model and results in a discrete algorithm even if the problem is of continuous nature as in the slider models. Extensive experimental results on both realworld instances and point sets created by a widely used benchmark generator show that the new approach is applicable in practice. 1
A Minimal Line Property Preserving Representation of Line Images
 Computing
, 1999
"... . In line image understanding a minimal line property preserving (MLPP) graph of the image compliments the structural information in geometric graph representations liketherun graph. With such a graph and its dual it is possible to efficiently detect topological features like loops and holes and to ..."
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Cited by 12 (4 self)
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. In line image understanding a minimal line property preserving (MLPP) graph of the image compliments the structural information in geometric graph representations liketherun graph. With such a graph and its dual it is possible to efficiently detect topological features like loops and holes and to make use of relations like containment. We present a new rule based method on dual graph contraction for transforming the run graph and its dual into MLPP graphs. A parallel O(log(longest curve)) algorithm is presented and results given. 1
An Efficient Algorithm for Weakly Normal Dominance Constraints
 In ACMSIAM Symposium on Discrete Algorithms
, 2004
"... Dominance constraints are logical descriptions of trees. E cient algorithms for the subclass of normal dominance constraints were proposed recently. We present a new and simpler graph algorithm which solves more expressive weakly normal dominance constraints. We thereby improve on the best prev ..."
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Cited by 12 (1 self)
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Dominance constraints are logical descriptions of trees. E cient algorithms for the subclass of normal dominance constraints were proposed recently. We present a new and simpler graph algorithm which solves more expressive weakly normal dominance constraints. We thereby improve on the best previously known algorithm for normal dominance constraints in eciency, coverage, and applicability.
The Deferred Path Heuristic for the Generalized Tree Alignment Problem
 Journal of Computational Biology
, 1997
"... Many multiple alignment methods implicitly or explicitly try to minimize the amount of biological change implied by an alignment. At the level of sequences, biological change is measured along a phylogenetic tree, a structure frequently being predicted only after the multiple alignment instead of ..."
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Cited by 11 (3 self)
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Many multiple alignment methods implicitly or explicitly try to minimize the amount of biological change implied by an alignment. At the level of sequences, biological change is measured along a phylogenetic tree, a structure frequently being predicted only after the multiple alignment instead of together with it. The Generalized Tree Alignment problem addresses both questions simultaneously. It can formally be viewed as a Steiner tree problem in sequence space and our approach merges a path heuristic for the construction of a Steiner tree with a clustering method as usually applied only to distance data. This combination is achieved using sequence graphs, a data structure for efficient representation of similar sequences. Although somewhat slower in practice than an earlier method by Hein (Mol. Biol. Evol., 6:649668,1989) the current approach achieves significantly better results in terms of the underlying scoring function. Furthermore, a variant of the algorithm is intr...
Maintaining Shortest Paths in Digraphs with Arbitrary Arc Weights: An Experimental Study
 In Proc. Workshop on Algorithm Engineering
, 2000
"... We present the first experimental study of the fully dynamic singlesource shortest paths problem in digraphs with arbitrary (negative and nonnegative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus ..."
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Cited by 11 (2 self)
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We present the first experimental study of the fully dynamic singlesource shortest paths problem in digraphs with arbitrary (negative and nonnegative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus a new algorithm devised to be as simple as possible while matching the best worstcase bounds for the problem. According to experiments performed on randomly generated test sets, all the considered dynamic algorithms are faster by several orders of magnitude than recomputing from scratch with the best static algorithm. The experiments also reveal that, although the simple dynamic algorithm we suggest is usually the fastest in practice, other dynamic algorithms proposed in the literature yield better results for specific kinds of test sets. 1
Certifying Algorithms
, 2010
"... A certifying algorithm is an algorithm that produces, with each output, a certificate or witness (easytoverify proof) that the particular output has not been compromised by a bug. A user of a certifying algorithm inputs x, receives the output y and the certificate w, and then checks, either manual ..."
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Cited by 10 (2 self)
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A certifying algorithm is an algorithm that produces, with each output, a certificate or witness (easytoverify proof) that the particular output has not been compromised by a bug. A user of a certifying algorithm inputs x, receives the output y and the certificate w, and then checks, either manually or by use of a program, that w proves that y is a correct output for input x. In this way, he/she can be sure of the correctness of the output without having to trust the algorithm. We put forward the thesis that certifying algorithms are much superior to noncertifying algorithms, and that for complex algorithmic tasks, only certifying algorithms are satisfactory. Acceptance of this thesis would lead to a change of how algorithms are taught and how algorithms are researched. The widespread use of certifying algorithms would greatly enhance the reliability of algorithmic software. We survey the state of the art in certifying algorithms and add to it. In particular, we start a
From Algorithms to Working Programs On the Use of Program Checking in LEDA
 IN PROC. INT. CONF. ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS 98
, 1998
"... We report on the use of program checking in the LEDA library of efficient data types and algorithms. ..."
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Cited by 9 (2 self)
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We report on the use of program checking in the LEDA library of efficient data types and algorithms.