Download e-book for iPad: Algorithm Theory - SWAT 2002 by Penttonen M., Schmidt E.M.

By Penttonen M., Schmidt E.M.

This e-book constitutes the refereed lawsuits of the eighth Scandinavian Workshop on set of rules concept, SWAT 2002, held in Turku, Finland, in July 2002.The forty three revised complete papers provided including invited contributions have been rigorously reviewed and chosen from 103 submissions. The papers are geared up in topical sections on scheduling, computational geometry, graph algorithms, robotics, approximation algorithms, facts conversation, computational biology, and knowledge garage and manipulation.

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Define e(i, ) = cπ (i − 1) + d(pπ(i−1) , p ), f = min{i | r ≤ e(i, ), p ∈ pπ(i−1) ❀ pπ(i) }. Intuitively, e(i, ) is the earliest point in time that position p can be reached after servicing requests π(1), . . , π(i − 1). The vehicle crosses request for the first time after it becomes available when traveling from request π(f − 1) to request π(f ). f is well defined since p ∈ pπ(i−1) ❀ pπ(i) and r ≤ e(i, ) for i = π −1 ( ). If f = π −1 ( ) for all , then π is eager. Otherwise, there is some request with f < π −1 ( ).

Karuno, Nagamochi and Ibaraki give a 2-approximation algorithm for the single vehicle problem on trees. We develop a linear time PTAS for the single vehicle scheduling problem on trees which have a constant number of leaves. This PTAS can be easily adapted to accommodate various starting/ending constraints. We then extended this to a PTAS for the multiple vehicle problem where vehicles operate in disjoint subtrees. For this problem, the only previous result is a 2-approximation algorithm for paths [10].

We first prove structural results that show any preemptive schedule can be converted to a schedule with at most one preemption. Our algorithm converts an instance I of a preemptive problem into a pseudopolynomial number of nonpreemptive instances. One of these new instances has the optimal preemptive schedule of I as its optimal nonpreemptive schedule. The nonpreemptive version has a pseudopolynomial-time algorithm, so the optimal preemptive schedule can be found in pseudopolynomial time as well.

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Algorithm Theory - SWAT 2002 by Penttonen M., Schmidt E.M.


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