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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)
A classical topic in combinatorics is the study of problems of the following type: What are the maximum families F of subsets of a finite set with the property that the intersection of any two sets in the family satisfies some specified condition? Typical restrictions on the intersections F n F of any F and F' in F are: (i) FnF'# 0, where all FEF have k(More)
The covering radius R of a code is the maximal distance of any vector from the code. This work gives a number of new results concerning t[ n, k], the minimal covering radius of any binary code of length n and dimension k. For example r[ n, 41 and t [ n, 51 are determined exactly, and reasonably tight bounds on t[ n, k] are obtained for any k when n is(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 we(More)
It is standard practice among authors discussing the minimum spanning tree problem to refer to the work of Kruskal(1956) and Prim (1957) as the sources of the problem and its first efficient solutions, despite the citation by both of Boruvka (1926) as a predecessor. In fact, there are several apparently independent sources and algorithmic solutions of the(More)