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Subset sums
 JOURNAL OF NUMBER THEORY
, 1987
"... Suppose E>O and k> I. We show that if II> n,,(k. a) and.4 L Z,, satisfies IAl> ( ( l/k) + E)n then there is a subset B L A such that 0 < 1 BI <I, and xhi B h = 0 (in 2,). The case k = 3 solves a problem of Stalley and another problem of Erdős and Graham. For an integer HI> 0, le ..."
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Cited by 10 (2 self)
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Suppose E>O and k> I. We show that if II> n,,(k. a) and.4 L Z,, satisfies IAl> ( ( l/k) + E)n then there is a subset B L A such that 0 < 1 BI <I, and xhi B h = 0 (in 2,). The case k = 3 solves a problem of Stalley and another problem of Erdős and Graham. For an integer HI> 0
On the variance of subset sum estimation
 In Proc. 15th ESA, LNCS 4698
, 2007
"... For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. Mathematically, we are dealing with a set of weighted items and want to support queries to arbitrary subset sums. With unit weights, we can compute s ..."
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Cited by 13 (6 self)
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For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. Mathematically, we are dealing with a set of weighted items and want to support queries to arbitrary subset sums. With unit weights, we can compute
Multidimensional Subset Sum Problem
, 1997
"... This document is an informal description of our main results presented in the thesis [2]. We propose heuristic modifications to the successful use of Lenstra, Lenstra and Lovasz's LLL algorithm [4] to solving the Subset Sum (or knapsack) problem ..."
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Cited by 1 (1 self)
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This document is an informal description of our main results presented in the thesis [2]. We propose heuristic modifications to the successful use of Lenstra, Lenstra and Lovasz's LLL algorithm [4] to solving the Subset Sum (or knapsack) problem
Inverse Theorems for Subset Sums
, 1994
"... Let A be a finite set of integers. For h 1, let S h (A) denote the set of all sums of h distinct elements of A. Let S(A) denote the set of all nonempty sums of distinct elements of A. The direct problem for subset sums is to find lower bounds for jS h (A)j and jS(A)j in terms of jAj. The inverse p ..."
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Cited by 4 (0 self)
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Let A be a finite set of integers. For h 1, let S h (A) denote the set of all sums of h distinct elements of A. Let S(A) denote the set of all nonempty sums of distinct elements of A. The direct problem for subset sums is to find lower bounds for jS h (A)j and jS(A)j in terms of jAj. The inverse
Lecture Notes For Subset Sum
"... Subset sum is one of the very few arithmetic/numeric problems that we will discuss in this class. It has lot of interesting properties and is closely related to other NPcomplete problems like Knapsack. Even though Knapsack was one of the 21 problems proved to be NPComplete by Richard Karp in his s ..."
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Subset sum is one of the very few arithmetic/numeric problems that we will discuss in this class. It has lot of interesting properties and is closely related to other NPcomplete problems like Knapsack. Even though Knapsack was one of the 21 problems proved to be NPComplete by Richard Karp in his
The Multiple Subset Sum Problem
 SIAM JOURNAL OF OPTIMIZATION
, 1998
"... The Multiple Subset Sum Problem (MSSP) is the selection of items from a given ground set and their packing into a given number of identical bins such that the sum of the item weights in every bin does not exceed the bin capacity and the total sum of the weights of the items packed is as large as ..."
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Cited by 18 (1 self)
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The Multiple Subset Sum Problem (MSSP) is the selection of items from a given ground set and their packing into a given number of identical bins such that the sum of the item weights in every bin does not exceed the bin capacity and the total sum of the weights of the items packed is as large
The Complexity of Unary Subset Sum
"... Abstract. Given a stream of n numbers and a number B, the subset sum problem deals with checking whether there exists a subset of the stream that adds to exactly B. The unary subset sum problem, USS, is the same problem when the input is encoded in unary. We prove that any ppass randomized algorith ..."
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Abstract. Given a stream of n numbers and a number B, the subset sum problem deals with checking whether there exists a subset of the stream that adds to exactly B. The unary subset sum problem, USS, is the same problem when the input is encoded in unary. We prove that any ppass randomized
Database Security and Subset Sums
, 1998
"... We discuss applications of combinatorial arguments to database security: maximizing the “usability ” of a statistical database under the control of the mechanism Audit Expert of Chin and Ozsoyoglu. As modelled by Mirka Miller et al., the goal is to maximize the number of SUM queries from a database ..."
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of real numbers without compromising it. Via linear algebra, direct connections emerge between such database query models and problems that concern maximimizing, over all choices of n nonzero elements a1,..., an in Rm, the number of the 2n subset sums � i∈I ai, over all index sets I, belonging to some
On the Expressiveness of SubsetSum Representations
 Acta Inform
, 2000
"... We develop a general theory for representing information as sums of elements in a subset of the basic set A of numbers of cardinality n, often refered to as a "knapsack vector". How many numbers can be represented in this way depends heavily on A. The lower, resp. upper, bound for the c ..."
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We develop a general theory for representing information as sums of elements in a subset of the basic set A of numbers of cardinality n, often refered to as a "knapsack vector". How many numbers can be represented in this way depends heavily on A. The lower, resp. upper, bound
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems.
 Math. Programming
, 1993
"... We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of the L3algorithm of Lenstra, Lenstra, Lov'asz (1982). We present a variant of the L3 algorithm with "deep insertions" and a practical algorithm for block KorkinZ ..."
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Cited by 319 (7 self)
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Zolotarev reduction, a concept introduced by Schnorr (1987). Empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 66 random weights of arbitrary bit length within at most a few hours on a UNISYS 6000/70 or within a couple of minutes on a SPARC 1+ computer.
Results 1  10
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