We study the edge-disjoint escape problem in grids. Given a set of n sources in a two-dimensional grid, the problem is to connect all sources to the grid boundary using a set of n edge-disjoint paths. Different from t...
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We study the edge-disjoint escape problem in grids. Given a set of n sources in a two-dimensional grid, the problem is to connect all sources to the grid boundary using a set of n edge-disjoint paths. Different from the conventional approach, which reduces the problem to a network flow problem, we solve the problem by first ensuring that no rectangle in the grid contain more sources than outlets, a necessary and. sufficient condition for the existence of a solution. Based on this condition, we give a greedy algorithm that finds the paths in O(n(2)) time, which is faster than all previous approaches. This problem finds applications in point-to-point delivery, VLSI reconfiguration, and package routing.
This paper investigates multiprocessor-scheduling with machine constraints, which has many applications in the flexible manufacturing systems and in VLSI chip design. Machines have different starting times and each ma...
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ISBN:
(纸本)0819442836
This paper investigates multiprocessor-scheduling with machine constraints, which has many applications in the flexible manufacturing systems and in VLSI chip design. Machines have different starting times and each machine can schedule at most k jobs in a period. The objective is to minimizing the makespan. For this strogly NP-hard problem, it is important to design near-optimal approximation algorithms. It is known that Modified LPT algorithm has a worst-case ratio of 3/2 - 1/(2m) for k = 2 where m is the number of machines. For k > 2, no good algorithm has been got in the literature. In this paper, we prove the worst-case ratio of Modified LPT is less than 2. We further present an approximation algorithm Matching and show it has a worst-case ratio 2 - 1/m for every k > 2. By introducing parameters, we get two better worst-case ratios which show the Matching algorithm is near optimal for two special cases.
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