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36
Backwards Analysis of Randomized Geometric Algorithms
 Trends in Discrete and Computational Geometry, volume 10 of Algorithms and Combinatorics
, 1992
"... The theme of this paper is a rather simple method that has proved very potent in the analysis of the expected performance of various randomized algorithms and data structures in computational geometry. The method can be described as "analyze a randomized algorithm as if it were running backwards in ..."
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Cited by 60 (0 self)
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The theme of this paper is a rather simple method that has proved very potent in the analysis of the expected performance of various randomized algorithms and data structures in computational geometry. The method can be described as "analyze a randomized algorithm as if it were running backwards in time, from output to input." We apply this type of analysis to a variety of algorithms, old and new, and obtain solutions with optimal or near optimal expected performance for a plethora of problems in computational geometry, such as computing Delaunay triangulations of convex polygons, computing convex hulls of point sets in the plane or in higher dimensions, sorting, intersecting line segments, linear programming with a fixed number of variables, and others. 1 Introduction The curious phenomenon that randomness can be used profitably in the solution of computational tasks has attracted a lot of attention from researchers in recent years. The approach has proved useful in such diverse area...
A Minimal Algorithm for the MultipleChoice Knapsack Problem.
 European Journal of Operational Research
, 1994
"... The MultipleChoice Knapsack Problem is defined as a 01 Knapsack Problem with the addition of disjoined multiplechoice constraints. As for other knapsack problems most of the computational effort in the solution of these problems is used for sorting and reduction. But although O(n) algorithms whic ..."
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Cited by 43 (4 self)
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The MultipleChoice Knapsack Problem is defined as a 01 Knapsack Problem with the addition of disjoined multiplechoice constraints. As for other knapsack problems most of the computational effort in the solution of these problems is used for sorting and reduction. But although O(n) algorithms which solves the linear MultipleChoice Knapsack Problem without sorting have been known for more than a decade, such techniques have not been used in enumerative algorithms.
A minimal algorithm for the 01 Knapsack Problem.
 Operations Research
, 1994
"... Although several large sized 01 Knapsack Problems (KP) may be easily solved, it is often the case that most of the computational eort is used for preprocessing, i.e. sorting and reduction. In order to avoid this problem it has been proposed to solve the socalled core of the problem: A Knapsack ..."
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Cited by 41 (10 self)
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Although several large sized 01 Knapsack Problems (KP) may be easily solved, it is often the case that most of the computational eort is used for preprocessing, i.e. sorting and reduction. In order to avoid this problem it has been proposed to solve the socalled core of the problem: A Knapsack Problem de ned on a small subset of the variables. But the exact core cannot be identi ed without solving KP, so till now approximated core sizes had to be used.
Framework for Task Scheduling in Heterogeneous Distributed Computing Using Genetic Algorithms
 Artificial Intelligence Review
, 2004
"... An algorithm has been developed to dynamically schedule heterogeneous tasks on to heterogeneous processors in a distributed system. The scheduling strategy operates in a dynamically changing computing resource environment and adapts to variable communication costs and variable availability of proces ..."
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Cited by 22 (2 self)
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An algorithm has been developed to dynamically schedule heterogeneous tasks on to heterogeneous processors in a distributed system. The scheduling strategy operates in a dynamically changing computing resource environment and adapts to variable communication costs and variable availability of processing resources. The scheduler utilises a genetic algorithm to minimise the overall execution time. Experiments are performed which show that the algorithm can achieve near optimal efficiency, with up to 100,000 tasks being scheduled.
An expandingcore algorithm for the exact 01 Knapsack Problem.
 European Journal of Operational Research
, 1993
"... A new branchandbound algorithm for the exact solution of the 01 Knapsack Problem is presented. The algorithm is based on solving an "expanding core", which initially only contains the break item, but which is expanded each time the branchandbound algorithm reaches the border of the core. Comput ..."
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Cited by 21 (7 self)
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A new branchandbound algorithm for the exact solution of the 01 Knapsack Problem is presented. The algorithm is based on solving an "expanding core", which initially only contains the break item, but which is expanded each time the branchandbound algorithm reaches the border of the core. Computational experiments show that most data instances are optimally solved without sorting or preprocessing a great majority of the items. Detailed program sketches are provided, and computational experiments are reported, indicating that the algorithm presented not only is shorter, but also faster and more stable than any other algorithm hitherto proposed.
Total Path Length for Random Recursive Trees
, 1998
"... Total path length, or search cost, for a rooted tree is defined as the sum of all roottonode distances. Let T n be the total path length for a random recursive tree of order n. Mahmoud (1991) showed that W n := (T n \Gamma E[T n ])=n converges almost surely and in L 2 to a nondegenerate limiting ..."
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Cited by 19 (0 self)
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Total path length, or search cost, for a rooted tree is defined as the sum of all roottonode distances. Let T n be the total path length for a random recursive tree of order n. Mahmoud (1991) showed that W n := (T n \Gamma E[T n ])=n converges almost surely and in L 2 to a nondegenerate limiting random variable W . Here we give recurrence relations for the moments of W n and of W and show that W n converges to W in L p for each 0 ! p ! 1. We confirm the conjecture that the distribution of W is not normal. We also show that the distribution of W is characterized among all distributions having zero mean and finite variance by the distributional identity W d = U(1 +W ) + (1 \Gamma U)W \Gamma E(U); where E(x) := \Gammax ln x \Gamma (1 \Gamma x) ln(1 \Gamma x) is the binary entropy function, U is a uniform(0; 1) random variable, W and W have the same distribution, and U; W , and W are mutually independent. Finally, we derive an approximation for the distribution of W usi...
Engineering Radix Sort
 COMPUTING SYSTEMS
, 1993
"... Radix sorting methods have excellent asymptotic performance on string data, for which comparison is not a unittime operation. Attractive for use in large byteaddressable memories, these methods have nevertheless long been eclipsed by more easily programmed algorithms. Three ways to sort strings by ..."
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Cited by 15 (0 self)
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Radix sorting methods have excellent asymptotic performance on string data, for which comparison is not a unittime operation. Attractive for use in large byteaddressable memories, these methods have nevertheless long been eclipsed by more easily programmed algorithms. Three ways to sort strings by bytes left to righta stable list sort, a stable twoarray sort, and an inplace "American flag" sortare illustrated with practical C programs. For heavyduty sorting, all three perform comparably, usually running at least twice as fast as a good quicksort. We recommend American flag sort for general use.
An improved master theorem for divideandconquer recurrences
 In Automata, languages and programming
, 1997
"... Abstract. This paper presents new theorems to analyze divideandconquer recurrences, which improve other similar ones in several aspects. In particular, these theorems provide more information, free us almost completely from technicalities like floors and ceilings, and cover a wider set of toll fun ..."
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Cited by 12 (2 self)
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Abstract. This paper presents new theorems to analyze divideandconquer recurrences, which improve other similar ones in several aspects. In particular, these theorems provide more information, free us almost completely from technicalities like floors and ceilings, and cover a wider set of toll functions and weight distributions, stochastic recurrences included.
A Formally Verified Sorting Certifier
 IEEE Transactions on Computers
, 1997
"... In this paper we describe the use of the certificationtrail technique as the basis of a new hybrid framework for building formally verified software systems. Our technique involves formally verifying only a part of a software system; however, the technique yields a software system which still satis ..."
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Cited by 6 (1 self)
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In this paper we describe the use of the certificationtrail technique as the basis of a new hybrid framework for building formally verified software systems. Our technique involves formally verifying only a part of a software system; however, the technique yields a software system which still satisfies the most important correctness properties. Substantial savings in the overhead of software verification, and also in program running time are shown to be possible in comparison to traditional methods. We apply our technique to the problem of sorting since sorting represents one of the most basic operations in computer science, and a formally verified sorting certifier should have significant applicability. The results presented in this paper represent an enhancement of the certificationtrail technique relative to the detection of incorrect computational output caused by software faults. Index terms: Sorting; formal program verification; software correctness; certification trails; prog...