Algorithm Design for Computer System Design by G. Ausiello, M. Lucertini, P. Serafini (eds.)

By G. Ausiello, M. Lucertini, P. Serafini (eds.)

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1980. [42] HYAFIL, RIVEST: Graph partitioning and constructing optimal decision trees are polynomial complete problems. IRIA Rep. 33, 1973. [43] IBARRA, KIM: Fast approximation algorithms for the Knapsach and sum of subset problems. J. ACM, 1975 46 [44] M. Lucertini IBARRA, KIM: Approximation algorithms for certain scheduling problems. Math. Op. , 1978. [451 JENNY, KUMMERLE: Distributed processing within an integrated circuit/packet-switching node. IEEE Tr. , 1976. [46] JENSEN: Optimal network partitioning.

55] LAWLER: Cutsets and partitions of Hypergraphs Networks, 1973. [56] LAWLER: Fast approximation algorithms for Knapsack problems. Math. Op. , 1979. [57] LIPTON, TARJAN: A separator theorem for planar graphs. Conf. on Theor. , Waterloo, 1977. [58] LIPTON, TARJAN: Applications of a planar separator theorem. 18th FOCS. Long Beach, 1977. Models of the Task Assignment Problem in Distributed Systems [59] 47 LUCCIO, SAMI: On the decomposition of networks in minimally interconnected subnetworks. IEEE Tr.

If T is a star, ET can be solved in polynomial time by sorting (O(n log n)) (for any norm). In the general case ET with L norm can be '" solved in polynomial time. More precisely the problem of finding a 41 Models of the Task Assignment Problem in Distributed Systems mrpartition of T minimizing the maximum cluster weight can be solved by a shifting algorithm in time O(m 3rd(T)+m on) where rd(T) 1S the number of edges in the radius of T [2]. The easiest probl~m of finding a mrpartition of T maximizing the minimum cluster weight can be solved 1n time O(m2 rd(T)+mon) [66].

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