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Geometric Range Searching
, 1994
"... In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in c ..."
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Cited by 54 (2 self)
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In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in computational geometry, as they can be used as subroutines in many seemingly unrelated algorithms. We present a survey of results and main techniques in this area.
A Formal Approach to the Vertical Partitioning Problem in Distributed Database Design
 In Technical Report. CIS Dept, Univ. of
, 1993
"... The design of distributed databases is an optimization problem requiring solutions to several interrelated problems: data fragmentation, allocation, and local optimization. Each problem can be solved with several different approaches thereby making the distributed database design a very difficult ta ..."
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Cited by 12 (2 self)
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The design of distributed databases is an optimization problem requiring solutions to several interrelated problems: data fragmentation, allocation, and local optimization. Each problem can be solved with several different approaches thereby making the distributed database design a very difficult task. Although there is a large body of work on the design of data fragmentation, most of them are either ad hoc solutions or formal solutions for special cases (e. g., binary vertical partitioning). In this paper, we address the problem of nary vertical partitioning problem and derive an objective function that generalizes and subsumes earlier work. The objective function derived in this paper is being used for developing heuristic algorithms that can be shown to satisfy the objective function. The objective function is also being used for comparing previously proposed algorithms for vertical partitioning. We first derive an objective function that is suited to distributed transaction proces...
Algorithmic techniques for geometric optimization
 In Computer Science Today: Recent Trends and Developments, Lecture Notes in Computer Science
, 1995
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Calculation of Stability . . .
, 1997
"... We present algorithms to calculate the stability radius of optimal or approximate solutions of binary programming problems with a minsum or min{max objective function. Our algorithms run in polynomial time if the optimization problem itself is polynomially solvable. We also extend our results to th ..."
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We present algorithms to calculate the stability radius of optimal or approximate solutions of binary programming problems with a minsum or min{max objective function. Our algorithms run in polynomial time if the optimization problem itself is polynomially solvable. We also extend our results to the tolerance approach to sensitivity analysis.