On single row routing

Saxena, Sanjeev; Prasad, V.C.

doi:10.1109/31.31342

Cited by 3 publications

(1 citation statement)

References 11 publications

(5 reference statements)

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“…Due to the bottleneck of computing connected components and spanning trees, the resulting parallel implementation runs in O(1og n loglog n ) time using n processors in the CRCW model of computation. In the light of the O(n) sequential algorithm, the parallel algorithm of [25] is, clearly, not cost-optimal.…”

Section: Introductionmentioning

confidence: 98%

A time- and cost-optimal algorithm for interlocking sets-with applications

Olariu

Zomaya²

1996

IEEE Trans. Parallel Distrib. Syst.

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Given a family l o f intervals, two intervals in Iinterlock if they overlap but neither of them strictly contains the other. A set of intervals in which every two are related in the reflexive transitive closure of the interlock relation is referred to as an interlocking set. The task is determining the maximal interlocking sets of Iarises in numerous applications, including traffic control, robot arm manipulation, segmentation of range images, routing, automated surveillance systems, recognizing polygonal configurations, and code generation for parallel machines. Our first contribution is to show that any sequential algorithm that computes the maximal interlocking sets of a family of n intervals must take Q(n log n) time in the algebraic tree model. Next, we show that any parallel algorithm for this problem must take Q(log n) time in the CREW model even if an infinite number of processors and memory cells are available. We then go on to show that both the sequential and the parallel lower bounds are tight by providing matching algorithms running, respectively, in @(n log n) sequential time and in @(log n) time using n processors in the CREW model. At the same time, if the endpoints of the intervals are specified in sorted order, our sequential algorithm runs in O(n) time, improving the best previously known result. It is interesting to note that even if the endpoints are sorted, R(log n) is a time lower bound for solving the problem in the CREW model, regardless of the amount of resources available. As an application of our algorithm for interlocking sets, we obtain a time-and cost-optimal solution to a restricted version of the single row routing problem. The best previously known result for routing a set of n nets without street crossovers runs in O(log n loglog n) time using n processors in the CRCW model. By contrast, our algorithm runs in @(log n) time using processors in the CREW model, being both time-and cost-optimal.

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Section: Introductionmentioning

confidence: 98%

A time- and cost-optimal algorithm for interlocking sets-with applications

Olariu

Zomaya²

1996

IEEE Trans. Parallel Distrib. Syst.

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A heuristic single-row router minimizing interstreet crossings

Batalama

Pados

Papatheodorou

1993

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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A time- and cost-optimal algorithm for overlap graphs, with applications

Olariu

Zomaya²

Proceedings of the 1996 ICPP Workshop on Challenges for Parallel Processing

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In varioui practical applications it is convenient to associate a cer I ain graph with a family Z of intervals. One such graph is the well-known overlap graphof Z, whose vertices are the iiitervals in I , with two intervals connected by and edge if imd only if they overlap but neither of them strictly contains the other. The first main contribution of this paper is to propose time-and cost-optimal algorithms for computiiig the connected components of an overlap graph. The iask of computing the connected components of an overlap graph arises in numerous applications including traffic control, robot arm manipulation, segmentation of range images, routing, automated surveillance systems, recognizing polygonal configurations, and code generation for parallel niachines. We begin by showing that any sequential algo i ithm that determines the connected components of the overlap graph of a family of n intervals must take L?(nlog r j ) time in the algebraic tree model. Next, we show that any parallel algorithm for this problem must take L?(logn'i time in the CREW model even if an infinite numbei of processors and meinoiy cells are available. We then go on to show that both the sequential and the parallel lowei bounds are tight by providing matching algorithms running in @ ( n log n ) sequential time and @(log n ) time using n processors in the CREW model, respectively. At the same time, if the endpoints of the intervals are given in sorted ordLi. our sequential algorithm runs in @ ( n ) time, improving the best previously known result. It is interesting to note t l i i L t even if the endpoints are sorted, R(1og n ) is a time lower hound for solving the problem in the CREW model, regaicllrss of the amount of resources available. As an application, we show t h a t our algorithm affords us a time-and cost-optimal solution to a restricted version of the single row routing problem. The best previously known result for routing a set of nets without interstreet crossings run5 in O(1og n log log n ) time using n processors in the CRCT7I model. By contrast, our algorithm runs in ~

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On single row routing

Cited by 3 publications

References 11 publications

A time- and cost-optimal algorithm for interlocking sets-with applications

A time- and cost-optimal algorithm for interlocking sets-with applications

A heuristic single-row router minimizing interstreet crossings

A time- and cost-optimal algorithm for overlap graphs, with applications

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