By Penttonen M., Schmidt E.M.
This booklet constitutes the refereed court cases of the eighth Scandinavian Workshop on set of rules idea, SWAT 2002, held in Turku, Finland, in July 2002.The forty three revised complete papers awarded including invited contributions have been rigorously reviewed and chosen from 103 submissions. The papers are prepared in topical sections on scheduling, computational geometry, graph algorithms, robotics, approximation algorithms, facts communique, computational biology, and knowledge garage and manipulation.
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As with σ ↓ , in σ ↑ there is an additional request at the origin, the 0th request, with p↑0 = p0 , r0↑ = 0 and h↑0 = δ. Using the algorithm described in the preceding section, we can solve σ ↓ exactly in time O(n (a + 1)(b + 2t − 1)(t+1)a+1 ) = O(n (8(t + 1) 1/ 2 + 2t − 1)2(t+1) 1/ +1 / ), which is linear in n for constant t and . We now observe that an optimal schedule π for σ ↓ is also an optimal schedule for σ ↑ . Intuitively, problem σ ↑ is the same as problem σ ↓ but with all requests except 0 shifted back δ time units.
Several special cases have polynomial-time algorithms. When preemption is allowed, hardness results depend on the type of preemption allowed. For all three objective functions, the Lazy Bureaucrat Scheduling Problem is polynomially solvable under pmtnI , weakly NP-complete under pmtnII , and strongly NP-complete under pmtnIII . Open problems include ﬁnding algorithms for 1 | lazy, pmtnII | Cmax , 1 | lazy, pmtnII | ij tij , and 1 | lazy, pmtnII | j wj (1 − Uj ) that run in pseudopolynomial time, with or without release dates.
2001), pp. 218– 229. 11. , and Nagamochi, H. A polynomial time approximation scheme for the multi-vehicle scheduling problem on a path with release and handling times. In Proceedings of the 12th International Symposium on Algorithms and Computation (Dec. 2001), pp. 36–47. 12. , and Ibaraki, T. Vehicle scheduling on a tree with release and handling times. Annals of Operations Research 69 (1997), 193–207. 13. , and Ibaraki, T. 5-approximation for singlevehicle scheduling problem on a line with release and handling times.