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10,857
Efficient Representation of Integer Sets
- DCC - FC & LIACC, Universidade do
, 2006
"... Efficient representation of integer ..."
Integer sets containing no arithmetic progressions
- J. London Math. Soc
, 1987
"... lfh and k are positive integers there exists N(h, k) such that whenever N ^ N(h, k), and the integers 1,2,...,N are divided into h subsets, at least one must contain an arithmetic progression of length k. This is the famous theorem of van der Waerden [10], dating from 1927. The proof of this uses mu ..."
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Cited by 76 (0 self)
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lfh and k are positive integers there exists N(h, k) such that whenever N ^ N(h, k), and the integers 1,2,...,N are divided into h subsets, at least one must contain an arithmetic progression of length k. This is the famous theorem of van der Waerden [10], dating from 1927. The proof of this uses
INTEGER SETS WITH DISTINCT SUBSET SUMS
"... Abstract. We give a simple, elementary new proof of a generalization of the following conjecture of Paul Erdős: the sum of the elements of a finite integer set with distinct subset sums is less than 2. Let a0 <a1<···<anbe positive integers with all the sums ∑n i=0 εiai (εi =0;1) different. ..."
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Abstract. We give a simple, elementary new proof of a generalization of the following conjecture of Paul Erdős: the sum of the elements of a finite integer set with distinct subset sums is less than 2. Let a0 <a1<···<anbe positive integers with all the sums ∑n i=0 εiai (εi =0;1) different
An integer set library for program analysis
- In: Advances in the Theory of Integer Linear Optimization and its Extensions, AMS 2009 Spring Western Section Meeting
, 2009
"... Many program analysis techniques are based on manipulations of sets of integers bounded by linear constraints. These integers typically represent iterations of a loop nest or elements of an array. Double description based libraries are sometimes used for representing such sets, but these libraries u ..."
Abstract
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Cited by 1 (0 self)
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Many program analysis techniques are based on manipulations of sets of integers bounded by linear constraints. These integers typically represent iterations of a loop nest or elements of an array. Double description based libraries are sometimes used for representing such sets, but these libraries
On mixed-integer sets with two integer variables
, 2010
"... We show that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with two integer variables is a crooked cross cut (which we defined recently in [3]). We then extend this observation to show that crooked cross cuts give the convex hull of mixed-integer sets with more ..."
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Cited by 1 (1 self)
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We show that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with two integer variables is a crooked cross cut (which we defined recently in [3]). We then extend this observation to show that crooked cross cuts give the convex hull of mixed-integer sets
INTEGER SETS WITH IDENTICAL REPRESENTATION FUNCTIONS
"... Abstract. We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions. Let N0 denote the set of all non-negative integers. To every subset A ⊆ N0 corre-sponds its representation fun ..."
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Abstract. We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions. Let N0 denote the set of all non-negative integers. To every subset A ⊆ N0 corre-sponds its representation
Tightening simple mixed-integer sets with guaranteed bounds
, 2008
"... In this paper we study how to reformulate knapsack sets and simple mixed integer sets in order to obtain provably tight, polynomially large formulations. 1 ..."
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Cited by 7 (3 self)
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In this paper we study how to reformulate knapsack sets and simple mixed integer sets in order to obtain provably tight, polynomially large formulations. 1
On Optimal Subset Representations of Integer Sets
- J. Number Theory
, 2000
"... In this paper, we investigate representations of sets of integers as subset sums of other sets of minimal size, achieving results on the nature of the representing set as well as providing several reformulations of the problem. We apply one of these reformulations to prove a conjecture and extend ..."
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Cited by 6 (0 self)
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In this paper, we investigate representations of sets of integers as subset sums of other sets of minimal size, achieving results on the nature of the representing set as well as providing several reformulations of the problem. We apply one of these reformulations to prove a conjecture
Predecessor Queries in Dynamic Integer Sets
, 1997
"... We consider the problem of maintaining a set of n integers in the range 0::2 w \Gamma 1 under the operations of insertion, deletion, predecessor queries, minimum queries and maximum queries on a unit cost RAM with word size w bits. Let f(n) be an arbitrary nondecreasing smooth function satisf ..."
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Cited by 4 (0 self)
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We consider the problem of maintaining a set of n integers in the range 0::2 w \Gamma 1 under the operations of insertion, deletion, predecessor queries, minimum queries and maximum queries on a unit cost RAM with word size w bits. Let f(n) be an arbitrary nondecreasing smooth function
Results 1 - 10
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10,857
