Ronald L. Graham

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The following abstract problem models several practical problems in computer science and operations research: given a list L of real numbers between 0 and 1, place the elements of L into a minimum number L* of "bins" so that no bin contains numbers whose sum exceeds 1. Motivated by the likelihood that an excessive amount of computation will be required by(More)
Despite the recognized potential of multiprocessing little is known concerning the general problem of finding efficient algorithms which compute minimallength schedules for given computations and m≧2 processors. In this paper we formulate a general model of computation structures and exhibit an efficient algorithm for finding optimal nonpreemptive schedules(More)
Of particular interest are those B for which the maximum families consist of socalled “kernel systems,” i.e., the family of all supersets of some fixed set in B. For example, we show that the set of all (cyclic) translates of a block of consecutive integers in [n] is such a family. It turns out rather unexpectedly that many of the results we obtain here(More)
The present paper represents essentially a chapter in a forthcoming "Monographie" in the l Enseignement Mathématique series i ) with the title "Old and new problems and results in combinatorial number theory" by the above authors . Basically we will discuss various problems in elementary number theory, most of which have a combinatorial flavor . In general(More)
One well-studied model ofa multiprocessing system involves a fixed number n of identical abstract processors, a finite set of tasks to be executed, each requiring a specified amount of computation time, and a partial ordering on the tasks which requires certain tasks to be completed before certain others can be initiated. The nonpreemptive operation of the(More)