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15
Problems in Computational Geometry
 Packing and Covering
, 1974
"...  reproduced, stored In a retrieval system, or transmlt'ted, In any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the author. ..."
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Cited by 454 (2 self)
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 reproduced, stored In a retrieval system, or transmlt'ted, In any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the author.
Semantical considerations on FloydHoare Logic
, 1976
"... This paper deals with logics of programs. The objective is to formalize a notion of program description, and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlyi ..."
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Cited by 212 (10 self)
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This paper deals with logics of programs. The objective is to formalize a notion of program description, and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlying FloydHoare axiom systems independently of such systems. Other directions that such research might take are considered.
Bounds on the complexity of the longest common subsequence problem
 Journal of the ACM
, 1976
"... ABSTRACT The problem of finding a longest common subsequence of two strings is discussed This problem arises in data processing applications such as comparing two files and in genetic applications such as studying molecular evolution The ddlqculty of computing a longest common subsequence of two str ..."
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Cited by 66 (1 self)
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ABSTRACT The problem of finding a longest common subsequence of two strings is discussed This problem arises in data processing applications such as comparing two files and in genetic applications such as studying molecular evolution The ddlqculty of computing a longest common subsequence of two strings IS examined using the decision tree model of computation, m which vertices represent "equalunequal " comparisons It IS shown that unless a bound on the total number of 0istmct symbols is assumed, every solution to the problem can consume an amount of time that is proportional to the product of the lengths of the two strings A general lower bound as a function of the ratio of alphabet size to string length is derived The case where comparisons between symbols of the same string are forbidden is also considered and it is shown that this problem is of linear complexity for a twosymbol alphabet and quadratic for an alphabet of three or more symbols KEY WORDS AND PHR~tSES longest common subsequence, algorithm, computational complexity, file comparison, molecular evolution CR CATEGORIES 3 12, 3 73, 5 25 1.
A TimeSpace Tradeoff for Sorting on NonOblivious Machines
, 1981
"... This paper adopts the latter strategy in order to pursue the complexity of sorting ..."
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Cited by 24 (2 self)
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This paper adopts the latter strategy in order to pursue the complexity of sorting
On Showing Lower Bounds for ExternalMemory Computational Geometry Problems
"... . In this paper we consider lower bounds for externalmemory computational geometry problems. We find that it is not quite clear which model of computation to use when considering such problems. As an attempt of providing a model, we define the external memory Turing machine model, and we derive low ..."
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Cited by 22 (4 self)
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. In this paper we consider lower bounds for externalmemory computational geometry problems. We find that it is not quite clear which model of computation to use when considering such problems. As an attempt of providing a model, we define the external memory Turing machine model, and we derive lower bounds for a number of problems, including the element distinctness problem, in this model. For these lower bounds we make the standard assumption that records are indivisible. Waiving the indivisibility assumption we show how to beat the lower bound for element distinctness. As an alternative model, we briefly discuss an externalmemory version of the algebraic computation tree. 1. Introduction The Input/Output (or just I/O) communication between fast internal memory and slower external storage is the bottleneck in many largescale computations. The significance of this bottleneck is increasing as internal computation gets faster, and as parallel computation gains popularity. Currently,...
Computational geometry  a survey
 IEEE TRANSACTIONS ON COMPUTERS
, 1984
"... We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis ofalgorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computeraided de ..."
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Cited by 19 (3 self)
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We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis ofalgorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computeraided design, computer graphics, operations research, pattern recognition, robotics, and statistics. Five major problem areasconvex hulls, intersections, searching, proximity, and combinatorial optimizationsare discussed. Seven algorithmic techniques incremental construction, planesweep, locus, divideandconquer, geometric transformation, pruneandsearch, and dynamizationare each illustrated with an example.Acollection of problem transformations to establish lower bounds for geometric problems in the algebraic computation/decision model is also included.
A timespace tradeoff for element distinctness
 SIAM Journal on Computing
, 1987
"... Abstract. In A time space tradeoff for sorting on nonoblivious machines, Borodin et al. [J. Comput. System Sci., 22 (1981), pp. 351364] proved that to sort n elements requires TS =fl(n 2) where T=time and S space on a comparison based branching program. Although element distinctness and sorting ar ..."
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Cited by 16 (0 self)
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Abstract. In A time space tradeoff for sorting on nonoblivious machines, Borodin et al. [J. Comput. System Sci., 22 (1981), pp. 351364] proved that to sort n elements requires TS =fl(n 2) where T=time and S space on a comparison based branching program. Although element distinctness and sorting are equivalent problems on a computation tree, the stated tradeoff result does not immediately follow for element distinctness or indeed for any decision problem. In this paper, we are able to show that TS fl(n3/2vg n) for deciding element distinctness (or the sign of a permutation). Key words, timespace tradeoffs, computational complexity, time lower bounds, space lower bounds AMS(MOS) subject classification. 68Q25 1. Introduction. Timespace
Lower Bounds for Fundamental Geometric Problems
 IN 5TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA'97
, 1996
"... We develop lower bounds on the number of primitive operations required to solve several fundamental problems in computational geometry. For example, given a set of points in the plane, are any three colinear? Given a set of points and lines, does any point lie on a line? These and similar question ..."
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Cited by 8 (0 self)
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We develop lower bounds on the number of primitive operations required to solve several fundamental problems in computational geometry. For example, given a set of points in the plane, are any three colinear? Given a set of points and lines, does any point lie on a line? These and similar questions arise as subproblems or special cases of a large number of more complicated geometric problems, including point location, range searching, motion planning, collision detection, ray shooting, and hidden surface removal. Previously these problems were studied only in general models of computation, but known techniques for these models are too weak to prove useful results. Our approach is to consider, for each problem, a more specialized model of computation that is still rich enough to describe all known algorit...
The Complexity Of Querying Indefinite Information: Defined Relations, Recursion And Linear Order
, 1992
"... This dissertation studies the computational complexity of answering queries in logical databases containing indefinite information arising from two sources: facts stated in terms of defined relations, and incomplete information about linearly ordered domains. First, we consider databases consisting ..."
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Cited by 7 (0 self)
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This dissertation studies the computational complexity of answering queries in logical databases containing indefinite information arising from two sources: facts stated in terms of defined relations, and incomplete information about linearly ordered domains. First, we consider databases consisting of (1) a DATALOG program and (2) a description of the world in terms of the predicates defined by the program as well as the basic predicates. The query processing problem in such databases is related to issues in database theory, including view updates and DATALOG optimization, and also to the Artificial Intelligence problems of reasoning in circumscribed theories and sceptical abductive reasoning. If the program is nonrecursive, the meaning of the database can be represented by Clark's Predicate Completion,...