A single-machine scheduling problem with precedence delays is analyzed. A set of n tasks is to be scheduled on the machine in such a way that the makespan is minimized. The executions of the tasks are constrained by p...
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A single-machine scheduling problem with precedence delays is analyzed. A set of n tasks is to be scheduled on the machine in such a way that the makespan is minimized. The executions of the tasks are constrained by precedence delays, i.e., a task can start its execution only after any of its predecessors has completed and the delay between the two tasks has elapsed. In the case of unit execution times and integer lengths of delays, the problem is shown to be NP-hard in the strong sense. In the case of integer execution times and unit length of delays, the problem is polynomial, and an O(n(2)) optimal algorithm is provided. Both preemptive and non-preemptive cases are considered.
The quality q of a numerical algorithm using some specified information is the ratio of its error to the smallest possible error of an algorithm based on the same information. We use as information function values al ...
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The quality q of a numerical algorithm using some specified information is the ratio of its error to the smallest possible error of an algorithm based on the same information. We use as information function values al equidistant points, periodicity and a Sound for the rth derivative. We show that q is rather small, ii the algorithm is based on spline interpolation.
A unilied vector sorting algorithm (VSA) is proposed, which sorts N arbitrary num-bers with clog. N-bits on an SIMD multi-processor system (SMMP) with processors and a composite interconnected network in time, where c...
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A unilied vector sorting algorithm (VSA) is proposed, which sorts N arbitrary num-bers with clog. N-bits on an SIMD multi-processor system (SMMP) with processors and a composite interconnected network in time, where c is an arbitrary positive constant. When is an arbitrary small posi-tive constant and u = log2 N, it is an O(logN) algorithm and when it is an optimal algorithm,pT = O(N log N)); where u = 1, c = 1 and e = 0.5 (a constant).
The paper deals with estimating linear continuous functionals on unitary spaces from inaccurate information, with applications to recovering band-limited signals. We show how the minimal estimation error depends on a ...
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The paper deals with estimating linear continuous functionals on unitary spaces from inaccurate information, with applications to recovering band-limited signals. We show how the minimal estimation error depends on a bound on data perturbations and specify the form of an optimal algorithm.
Given a two-dimensional point set rho, a chain C is a subset of rho in which for every two points one is dominated by the other. A k-chain is a subset of rho that can be partitioned into k-chains. The size of a k-chai...
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Given a two-dimensional point set rho, a chain C is a subset of rho in which for every two points one is dominated by the other. A k-chain is a subset of rho that can be partitioned into k-chains. The size of a k-chain is the total number of its points. A k-chain with maximum size, among all possible k-chains, is called a maximum k-chain. First geometric properties of k-chains are studied for an arbitrary k. Then a THETA(n log n)-time algorithm is presented for finding a maximum three-chain in a point set rho, where n = Absolute value of rho.
In this paper,we study the problem,of calculating the minimum collision distance between two planar convex polygons when one of them moves to another along a given ***,several novel concepts and properties are explore...
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In this paper,we study the problem,of calculating the minimum collision distance between two planar convex polygons when one of them moves to another along a given ***,several novel concepts and properties are explored,then an optimal algorithm OPFIV with time complexity O(log(n+m))is developed and its correctness and optimization are proved rigorously.
For any fixed1 k > 0, we obtain (a) an O(alpha2 log alpha log(k)n) time parallel algorithm for (alpha + 1) coloring an alpha-degree graph with n/log(k)n processors on an EREW PRAM, (b) an O(alpha2 log alpha log(k)n...
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For any fixed1 k > 0, we obtain (a) an O(alpha2 log alpha log(k)n) time parallel algorithm for (alpha + 1) coloring an alpha-degree graph with n/log(k)n processors on an EREW PRAM, (b) an O(alpha2 log alpha log(k)n) time parallel algorithm for 3-coloring an alpha-degree rooted tree with n/log(k)n processors on a CREW PRAM, (c) an O(log(k)n) time parallel algorithm for finding a Maximal Independent Set of a rooted tree on an ARBITRARY CRCW PRAM.
Star graphs, as discussed in [1], are considered to be attractive alternatives for hypercubes. In this paper, we discuss optimal data exchange algorithms for star graphs of small dimension (n less-than-or-equal-to 6)....
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Star graphs, as discussed in [1], are considered to be attractive alternatives for hypercubes. In this paper, we discuss optimal data exchange algorithms for star graphs of small dimension (n less-than-or-equal-to 6). In particular we study odd-distance and total exchange algorithms, using the tabular method introduced in [2]. The algorithms use no intermediate buffering of messages.
The core of a graph G is a path P in G that is central with respect to the property of minimizing d(P) = Sigma(v is an element of V) d(v, P), where d(v, P) is the distance of vertex v from P. We present an optimal par...
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The core of a graph G is a path P in G that is central with respect to the property of minimizing d(P) = Sigma(v is an element of V) d(v, P), where d(v, P) is the distance of vertex v from P. We present an optimal parallel algorithm for finding a core of a tree. The algorithm requires O(log n) time using n/log n processors on the EREW PRAM.
This paper presents a new approach for the following collision detection problem in the plane: Let a simple polygon P rotate at a center o with constant angular velocity omega and translate towards a set of polygonal ...
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This paper presents a new approach for the following collision detection problem in the plane: Let a simple polygon P rotate at a center o with constant angular velocity omega and translate towards a set of polygonal obstacles S with constant velocity nu. Given P and S as well as their initial positions, and given also the velocities of P, determine whether or not P will collide with any element of S and report the collided elements of S if collisions occurred. An O(mn) worst-case optimal algorithm is proposed to solve this problem, where n is the number of vertices of P and m is the number of vertices of the obstacles in S.
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