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11,086
Reconfigurable Accelerators for Combinatorial Problems
"... this article. In comparison to these projects, we use backtracking architectures with deduction strategies that range from the simple basic architecture via don't cares to Boolean constraint propagation. One advantage of our basic architecture is that the formula can be any Boolean expression, ..."
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this article. In comparison to these projects, we use backtracking architectures with deduction strategies that range from the simple basic architecture via don't cares to Boolean constraint propagation. One advantage of our basic architecture is that the formula can be any Boolean expression, and not necessarily in conjunctive normal form. We acknowledge that related work includes more powerful deduction strategies. However, a major feature of our accelerator is that we can oer dierent strategies that also have dierent hardware requirements. Thus we can select the strategy also depending on the available recongurable resources
Edmonds polytopes and a hierarchy of combinatorial problems
, 2006
"... Let S be a set of linear inequalities that determine a bounded polyhedron P. The closure of S is the smallest set of inequalities that contains S and is closed under two operations: (i) taking linear combinations of inequalities, (ii) replacing an inequality Σaj xj ≤ a0, where a1,a2,...,an are integ ..."
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prove that Σcj xj ≤ c0 belongs to the closure of S. To each integer linear programming problem, we assign a nonnegative integer, called its rank. (The rank is the minimum number of iterations of the operation (ii) that are required in order to eliminate the integrality constraint.) We prove
A combinatorial problem in matching
 and (2 ) 1
, 1969
"... The following problems were suggested by Taussky and Todd [6]. Let X =(*! , x2,..., xn) and Y =(yl,y2, ••,)>„) be two vectors. We say that X and Y match in r components if xt = yt for r values of /. We say that X covers Y if r ^ n — 1. Let G denote the set of /? " vectors (yi,y2, •••J ̂ n) ..."
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The following problems were suggested by Taussky and Todd [6]. Let X =(*! , x2,..., xn) and Y =(yl,y2, ••,)>„) be two vectors. We say that X and Y match in r components if xt = yt for r values of /. We say that X covers Y if r ^ n — 1. Let G denote the set of /? " vectors (yi,y2, •••J ̂ n
Combinatorial Problems in Chip Design
, 2008
"... The design of very large scale integrated (VLSI) chips is an exciting area of applying mathematics, posing constantly new challenges. We present some important and challenging open problems in various areas of chip design. Although the problems are motivated by chip design, they are formulated mathe ..."
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The design of very large scale integrated (VLSI) chips is an exciting area of applying mathematics, posing constantly new challenges. We present some important and challenging open problems in various areas of chip design. Although the problems are motivated by chip design, they are formulated
ON A COMBINATORIAL PROBLEM. II
, 1964
"... to possess property B if there exists a subset K of M so that no set of the family F is contained either in K or in K (K is the complement of K in M). HAJNAL and 1 [2] recently published a paper on the property B and its generalisations. One of the unsolved problems we state asks: What is the smalle ..."
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to possess property B if there exists a subset K of M so that no set of the family F is contained either in K or in K (K is the complement of K in M). HAJNAL and 1 [2] recently published a paper on the property B and its generalisations. One of the unsolved problems we state asks: What
On Parallel Algorithms for Combinatorial Problems
, 1993
"... Graphs are the most widely used of all mathematical structures. There is uncountable number of interesting computational problems defined in terms of graphs. A graph can be seen as a collection of vertices (V ), and a collection of edges (E) joining all or some of the vertices. One is very often int ..."
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Graphs are the most widely used of all mathematical structures. There is uncountable number of interesting computational problems defined in terms of graphs. A graph can be seen as a collection of vertices (V ), and a collection of edges (E) joining all or some of the vertices. One is very often
Combinatorial problems on subsets and their intersections
 Adv. Math., Suppl. Stud
, 1978
"... Let I S I = n, m(n; k l,k 2,k) respectively m'(n,k 1,k, k) denote the cardinali.ty of the largest family of subsets A i C S satisfying IA i I = k (respectively 1A í 1 S k) and 1A i n Ai 1 = k l or Z 2~ 912 * In this paper we prove a) m(n,0,k 2,k) (n), mI(n,0,k 2,k) 5 (2) + ntl; equality, iff k ..."
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Let I S I = n, m(n; k l,k 2,k) respectively m'(n,k 1,k, k) denote the cardinali.ty of the largest family of subsets A i C S satisfying IA i I = k (respectively 1A í 1 S k) and 1A i n Ai 1 = k l or Z 2~ 912 * In this paper we prove a) m(n,0,k 2,k) (n), mI(n,0,k 2,k) 5 (2) + ntl; equality, iff k = 2; b) m(n,0,k 2 ' k) s n, if k 2 X k, with equality for an infinity of n. For n a n o (k) we show that: nk nk a) m(n l,kVR2 ' k) 1, m ' (n,k l,k 2,k) s 1 + (n2 1) i 1; 2 2 b) more exactly, m(n,k,,R,2,k) s l infinity of n. nk l tik 2 kk l kk 2 with equality for an_4_ Trot integers 0 s Q1 s 2 2 < k < n be given. Denote by M(11,Q. l, k2 ' k) any maximal system a ={A i} of different sets such that 1 u A,1 1 n, IA i 1 = k ( Ai ea), n IA. Aj 1 = £ 1,k 2 ( A i,Aj E a, i # j), AA c.a
ON A COMBINATORIAL PROBLEM III
, 1969
"... A famiIy of sets { ACY} is said by MiIler [3] to have property B if there exists a set S which meets a11 the sets A and contains none of a them. Property B has been extensively studied in severa recent papers (see the references in [2] and the Iast chapter of P. Erd & and A. Hajnal, On chromatic ..."
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A famiIy of sets { ACY} is said by MiIler [3] to have property B if there exists a set S which meets a11 the sets A and contains none of a them. Property B has been extensively studied in severa recent papers (see the references in [2] and the Iast chapter of P. Erd & and A. Hajnal, On chromatic number of graphs and set systems, Acta. Math. Acad. Sci. Hung. 17 (1966) 6199). Hajnal and I define m(n) as the smaIIest integer for which there is a family of m(n) sets A k, IA, / = n, 1 ( k ( m(n), which do not have property B [1]. TriviaIly m(n) 5 ( 2n;i) (t a k e a11 subsets taken n at a time of a set of 2nl elements), m(2) = 3, m(3) = 7, m(4) is not known. It is known [Z], [a] that for n> ndd)
Combinatorial problems for Horn clauses
, 2007
"... Given a family of Horn clauses, what is the minimal number of Horn clauses implying all other clauses in the family? What is the maximal number of Horn clauses from the family without having resolvents of a certain kind? We consider various problems of this type, and give some sharp bounds. We also ..."
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Given a family of Horn clauses, what is the minimal number of Horn clauses implying all other clauses in the family? What is the maximal number of Horn clauses from the family without having resolvents of a certain kind? We consider various problems of this type, and give some sharp bounds. We also
Results 11  20
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11,086