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133
Paths Among Points Inside a Simple Polygon (Extended Abstract)
"... ) Marek Chrobak Gopalakrishnan Sundaram y Abstract In this paper we consider two problems in finding paths among a set X of points inside a simple polygon P . First, given two distinguished points s; t 2 X, we provide an algorithm which finds a simple path from s to t with vertices in X that do ..."
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) Marek Chrobak Gopalakrishnan Sundaram y Abstract In this paper we consider two problems in finding paths among a set X of points inside a simple polygon P . First, given two distinguished points s; t 2 X, we provide an algorithm which finds a simple path from s to t with vertices in X
Reconstructing Strings from Substrings
 Journal of Computational Biology
, 1993
"... this paper, we consider a variety of problems with application to sequencing by hybridization. First, we develop a theory of interactive sequencing by hybridization, based on ..."
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Cited by 34 (3 self)
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this paper, we consider a variety of problems with application to sequencing by hybridization. First, we develop a theory of interactive sequencing by hybridization, based on
Steiner Points in the Space of Genome Rearrangements
, 1996
"... We present some experiences with the problem of multiple genome comparison, analogous to multiple sequence alignment in sequence comparison, under the inversion and transposition distance metrics, given a fixed phylogeny. We first describe a heuristic for the case in which phylogeny is a star on thr ..."
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Cited by 18 (5 self)
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We present some experiences with the problem of multiple genome comparison, analogous to multiple sequence alignment in sequence comparison, under the inversion and transposition distance metrics, given a fixed phylogeny. We first describe a heuristic for the case in which phylogeny is a star on three vertices and then use this to approximate the multiple genome comparison problem via local search. Keywords Permutation reversals, chromosome inversions, median problem, phylogeny 1 Introduction Although the mathematical nature of the problems are very different, genome comparison has inherited much of the spirit of traditional research into sequence comparison. This paper explores the concept of multiple genome comparison, analogous to multiple sequence alignment in sequence comparison. And just as the original multiple alignment problem [17] was posed in terms of optimizing the internal nodes of a given phylogenetic tree by minimizing the sum of an edit distance over the branches of th...
A Partial Digest Approach to Restriction Site Mapping
 Bulletin of Mathematical Biology
, 1993
"... We present a new, practical algorithm to resolve the experimental data in restriction site analysis, which is a common technique for mapping DNA. Specifically, we assert that multiple digestions with a single restriction enzyme can provide sufficient information to identify the positions of the rest ..."
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Cited by 24 (2 self)
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We present a new, practical algorithm to resolve the experimental data in restriction site analysis, which is a common technique for mapping DNA. Specifically, we assert that multiple digestions with a single restriction enzyme can provide sufficient information to identify the positions of the restriction sites with high probability. The motivation for the new approach comes from combinatorial results on the number of mutually homeometric sets in one dimension, where two sets of n points are homeometric if the multiset of n(n \Gamma 1)=2 distances they determine are the same. Since experimental data contains error, we propose algorithms for reconstructing sets from noisy interpoint distances, including the possibility of missing fragments. We analyze the performance of these algorithms under a reasonable probability distribution, establishing a relative error limit of r = \Theta(1=n 2 ) beyond which our technique becomes infeasible. Through simulations, we establish that our techni...
Reconstructing Strings from Substrings in Rounds
 In Proc. 36th Symposium on Foundation of Computer Science (FOCS 95
, 1995
"... We establish a variety of combinatorial bounds on the tradeoffs inherent in reconstructing strings using few rounds of a given number of substring queries per round. These results lead us to propose a new approach to sequencing by hybridization (SBH), which uses interaction to dramatically reduce th ..."
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Cited by 20 (2 self)
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We establish a variety of combinatorial bounds on the tradeoffs inherent in reconstructing strings using few rounds of a given number of substring queries per round. These results lead us to propose a new approach to sequencing by hybridization (SBH), which uses interaction to dramatically reduce the number of oligonucleotides used for de novo sequencing of large DNA fragments, while preserving the parallelism which is the primary advantage of SBH. 1 Introduction Sequencing by hybridization (SBH) [4, 11] is a new and promising approach to DNA sequencing which offers the potential of reduced cost and higher throughput over traditional gelbased approaches. In this paper, we propose a new approach to sequencing by hybridization which permits the sequencing of arbitrarily large fragments without the inherently exponential chip area of SBH, while retaining the massive parallelism which is the primary advantage of the technique. We establish the potential of our technique through both ana...
Karyotype distributions in a stochastic model of reciprocal translocation
 Genome Research
, 1996
"... This article cites 6 articles, 3 of which can be accessed free at: service Email alerting click heretop right corner of the article or Receive free email alerts when new articles cite this article sign up in the box at the ..."
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Cited by 13 (7 self)
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This article cites 6 articles, 3 of which can be accessed free at: service Email alerting click heretop right corner of the article or Receive free email alerts when new articles cite this article sign up in the box at the
Generating Random Polygons with Given Vertices
, 1996
"... The problem of generating "random" geometric objects is motivated by the need to generate test instances for geometric algorithms. We examine the specific problem of generating a random xmonotone polygon on a given set of n vertices. Here, "random" is taken to mean that we sele ..."
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Cited by 14 (1 self)
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The problem of generating "random" geometric objects is motivated by the need to generate test instances for geometric algorithms. We examine the specific problem of generating a random xmonotone polygon on a given set of n vertices. Here, "random" is taken to mean that we select uniformly at random a polygon, from among all those xmonotone polygons having the given n vertices. We give an algorithm that generates a random monotone polygon in O(n) time and space after O(K) preprocessing time, where n ! K ! n 2 is the number of edges of the visibility graph of the xmonotone chain of the given vertex set. We also give an O(n 3 ) time algorithm for generating a random convex polygon whose vertices are a subset of a given set of n points. Finally, we discuss some further extensions, as well as the challenging open problem of generating random simple polygons. "Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin."  John v...
Counting Convex Polygons in Planar Point Sets
, 1992
"... Given a set S of n points in the plane, we compute in time O(n ) the total number of convex polygons whose vertices are a subset of S. We give an O(m n ) algorithm for computing the number of convex kgons with vertices in S, for all values k = 3; : : : ; m; previously known bounds were expon ..."
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Cited by 4 (1 self)
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Given a set S of n points in the plane, we compute in time O(n ) the total number of convex polygons whose vertices are a subset of S. We give an O(m n ) algorithm for computing the number of convex kgons with vertices in S, for all values k = 3; : : : ; m; previously known bounds were exponential (O(n )). We also compute the number of empty convex polygons (resp., kgons, k m) with vertices in S in time O(n ) (resp., O(m n )).
Efficient node overlap removal using a proximity stress model
 In 16th Symp. on Graph Drawing (GD
, 2008
"... Abstract. When drawing graphs whose nodes contain text or graphics, the nontrivial node sizes must be taken into account, either as part of the initial layout or as a postprocessing step. The core problem is to avoid overlaps while retaining the structural information inherent in a layout using li ..."
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Cited by 13 (6 self)
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Abstract. When drawing graphs whose nodes contain text or graphics, the nontrivial node sizes must be taken into account, either as part of the initial layout or as a postprocessing step. The core problem is to avoid overlaps while retaining the structural information inherent in a layout using little additional area. This paper presents a new node overlap removal algorithm that does well by these measures. 1
Recognizing Small Subgraphs
 Networks
, 1995
"... Although the general problem of subgraph isomorphism is NPcomplete, polynomialtime algorithms exist for recognizing any fixed subgraph. However, certain subgraphs appear easier to recognize than others. In this paper, we present general algorithms for fixedsubgraph isomorphism which improve or ..."
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Cited by 5 (0 self)
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Although the general problem of subgraph isomorphism is NPcomplete, polynomialtime algorithms exist for recognizing any fixed subgraph. However, certain subgraphs appear easier to recognize than others. In this paper, we present general algorithms for fixedsubgraph isomorphism which improve or unify previous results. In particular, we present an O(n m) algorithm for recognizing a fixed subgraph H with flower number f within a graph G with n vertices and m edges. Special cases of this algorithm match the best algorithms known for recognizing small paths, cycles, and cliques. Further, we improve previous results for recognizing C 5 and small even cycles C 2k , k 3.
Results 1  10
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