Results 1 
9 of
9
ClosestPoint Problems in Computational Geometry
, 1997
"... This is the preliminary version of a chapter that will appear in the Handbook on Computational Geometry, edited by J.R. Sack and J. Urrutia. A comprehensive overview is given of algorithms and data structures for proximity problems on point sets in IR D . In particular, the closest pair problem, th ..."
Abstract

Cited by 65 (14 self)
 Add to MetaCart
This is the preliminary version of a chapter that will appear in the Handbook on Computational Geometry, edited by J.R. Sack and J. Urrutia. A comprehensive overview is given of algorithms and data structures for proximity problems on point sets in IR D . In particular, the closest pair problem, the exact and approximate postoffice problem, and the problem of constructing spanners are discussed in detail. Contents 1 Introduction 1 2 The static closest pair problem 4 2.1 Preliminary remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Algorithms that are optimal in the algebraic computation tree model . 5 2.2.1 An algorithm based on the Voronoi diagram . . . . . . . . . . . 5 2.2.2 A divideandconquer algorithm . . . . . . . . . . . . . . . . . . 5 2.2.3 A plane sweep algorithm . . . . . . . . . . . . . . . . . . . . . . 6 2.3 A deterministic algorithm that uses indirect addressing . . . . . . . . . 7 2.3.1 The degraded grid . . . . . . . . . . . . . . . . . . ...
Combinatorial algorithms for DNA sequence assembly
 Algorithmica
, 1993
"... The trend towards very large DNA sequencing projects, such as those being undertaken as part of the human genome initiative, necessitates the development of efficient and precise algorithms for assembling a long DNA sequence from the fragments obtained by shotgun sequencing or other methods. The seq ..."
Abstract

Cited by 44 (3 self)
 Add to MetaCart
The trend towards very large DNA sequencing projects, such as those being undertaken as part of the human genome initiative, necessitates the development of efficient and precise algorithms for assembling a long DNA sequence from the fragments obtained by shotgun sequencing or other methods. The sequence reconstruction problem that we take as our formulation of DNA sequence assembly is a variation of the shortest common superstring problem, complicated by the presence of sequencing errors and reverse complements of fragments. Since the simpler superstring problem is NPhard, any efficient reconstruction procedure must resort to heuristics. In this paper, however, a four phase approach based on rigorous design criteria is presented, and has been found to be very accurate in practice. Our method is robust in the sense that it can accommodate high sequencing error rates and list a series of alternate solutions in the event that several appear equally good. Moreover it uses a limited form ...
Mechanical Translation of Set Theoretic Problem Specifications Into Efficient RAM Code  A Case Study
 Proc. EUROCAL 85
, 1985
"... This paper illustrates a fully automatic topdown approach to program development in which formal problem specifications are mechanically translated into efficient RAM code. This code is guaranteed to be totally correct and an upper bound on its worst case asymptotic running time is automatically de ..."
Abstract

Cited by 26 (8 self)
 Add to MetaCart
This paper illustrates a fully automatic topdown approach to program development in which formal problem specifications are mechanically translated into efficient RAM code. This code is guaranteed to be totally correct and an upper bound on its worst case asymptotic running time is automatically determined. The user is only required to supply the system with a formal problem specification, and is relieved of all responsibilities in the rest of the program development process. These results are obtained, in part, by greatly restricting the system to handle a class of determinate, set theoretic, tractable problems. The most essential transformational techniques that are used are fixed point iteration, finite differencing, and data structure selection. Rudimentary forms of these techniques have been implemented and used effectively in the RAPTS transformational programming system. This paper explains the conceptual underpinnings of our approach by considering the problem of attribute closure for relational databases and systematically deriving a program that implements a linear time solution. 1.
Finding MinimumCost Flows by Double Scaling
 MATHEMATICAL PROGRAMMING
, 1992
"... Several researchers have recently developed new techniques that give fast algorithms for the minimumcost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m arcs, maximum arc capacity U, and ..."
Abstract

Cited by 25 (4 self)
 Add to MetaCart
Several researchers have recently developed new techniques that give fast algorithms for the minimumcost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m arcs, maximum arc capacity U, and maximum arc cost magnitude C. The major techniques used are the capacityscaling approach of Edmonds and Karp, the excessscaling approach of Ahuja and Orlin, the costscaling approach of Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Taijan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (uncapacitated) transportation problem. In addition, we discuss a capacitybounding approach to the
Implementation of O(nm log n) Weighted Matchings in General Graphs  The Power of Data Structures
 IN WORKSHOP ON ALGORITHM ENGINEERING (WAE), LECTURE NOTES IN COMPUTER SCIENCE
, 2000
"... We describe the implementation of an O(nm log n) algorithm for weighted matchings in general graphs. The algorithm is a variant of the algorithm of Galil, Micali, and Gabow [GMG86] and requires the use of concatenable priority queues. No previous implementation had a worst{case guarantee of O(nm ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
We describe the implementation of an O(nm log n) algorithm for weighted matchings in general graphs. The algorithm is a variant of the algorithm of Galil, Micali, and Gabow [GMG86] and requires the use of concatenable priority queues. No previous implementation had a worst{case guarantee of O(nm log n). We compare our implementation to the experimentally fastest implementation (called Blossom IV) due to Cook and Rohe [CR97]; Blossom IV is an implementation of Edmonds' algorithm and has a running time no better than Ω(n³). Blossom IV requires only very simple data structures. Our experiments show that our new implementation is competitive to Blossom IV.
Towards Optimal Range Medians Beat Gfeller
, 901
"... We consider the following problem: given an unsorted array of n elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which uses O(n) space and needs O(n log k+k log n) time to answer the first k queri ..."
Abstract
 Add to MetaCart
We consider the following problem: given an unsorted array of n elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which uses O(n) space and needs O(n log k+k log n) time to answer the first k queries. This improves previous algorithms by a logarithmic factor and matches a lower bound for k = O(n). Since the algorithm decomposes the range of element values rather than the array, it has natural generalizations to higher dimensional problems – it reduces a range median query to a logarithmic number of range counting queries. 1 Introduction and Related Work The classical problem of finding the median is to find the element of rank ⌈n/2⌉ in an unsorted array of n elements. 1 Clearly, the median can be found in O(n log n) time by sorting the elements. However, a classical algorithm finds
The Visibility Graph Among Polygonal Obstacles: a Comparison of Algorithms
"... This paper examines differences of four approaches in finding the visibility graph of a polygonal region with obstacles defined by simple polygons. Each has been implemented and tuned. Experimental comparisons via time measurements have been carried out against a variety of testcases ranging in grap ..."
Abstract
 Add to MetaCart
This paper examines differences of four approaches in finding the visibility graph of a polygonal region with obstacles defined by simple polygons. Each has been implemented and tuned. Experimental comparisons via time measurements have been carried out against a variety of testcases ranging in graph density from maximal, O ( n 2), to minimal, W(n). In this manner, expected asymptotic time bounds have been verified with crossover points between the algorithms identified.
Implementing Dictionaries Using Hashing
, 1999
"... Introduction This chapter is based on Mehlhorn [5]. Many algorithms manipulate sets. For example, a compiler uses a symbol table to keep track of the identifiers that are used in a program. Identifiers are strings of letters and digits. With each identifier, associated information such as type, sco ..."
Abstract
 Add to MetaCart
Introduction This chapter is based on Mehlhorn [5]. Many algorithms manipulate sets. For example, a compiler uses a symbol table to keep track of the identifiers that are used in a program. Identifiers are strings of letters and digits. With each identifier, associated information such as type, scope, and address, is stored. As another example, the catalogue of a library maintains, among other things, names of authors. With each author, associated information such as title and ISBN number is stored. Typical operations that have to be supported in such applications are: access(x; S): if x 2 S, then return the information associated with x. Otherwise, report that x is not an element of S. insert(x; S): insert element x into S, i.e., set S := S [
EXACT AND APPROXIMATION ALGORITHMS
, 1991
"... This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon ..."
Abstract
 Add to MetaCart
This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper lefthand comer ana continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6 " x 9 " black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. U·M·I