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611,618
Set partitioning via inclusionexclusion
 SIAM J. Comput
"... Abstract. Given a set N with n elements and a family F of subsets, we show how to partition N into k such subsets in 2nnO(1) time. We also consider variations of this problem where the subsets may overlap or are weighted, and we solve the decision, counting, summation, and optimisation versions of t ..."
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Cited by 60 (7 self)
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of these problems. Our algorithms are based on the principle of inclusion–exclusion and the zeta transform. In effect we get exact algorithms in 2nnO(1) time for several wellstudied partition problems including Domatic Number, Chromatic Number, Maximum kCut, Bin Packing, List Colouring, and the Chromatic
Set MultiCovering via InclusionExclusion
"... Set multicovering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose ..."
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Cited by 3 (2 self)
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propose a family of exact algorithms for the set multicovering problem based on the inclusionexclusion principle. The presented ESMC (Exact Set MultiCovering) algorithm takes * n O ((2 t) ) time and * n O ( ( t + 1) ) space where t is the maximum value in the coverage requirement set (The * O ( f ( n
Parametric Shape Analysis via 3Valued Logic
, 2001
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
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Cited by 660 (79 self)
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Shape Analysis concerns the problem of determining "shape invariants"...
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
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Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
Approximate InclusionExclusion
 Combinatorica
, 1993
"... The InclusionExclusion formula expresses the size of a union of a family of sets in terms of the sizes of intersections of all subfamilies. This paper considers approximating the size of the union when intersection sizes are known for only some of the subfamilies, or when these quantities are giv ..."
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Cited by 52 (4 self)
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The InclusionExclusion formula expresses the size of a union of a family of sets in terms of the sizes of intersections of all subfamilies. This paper considers approximating the size of the union when intersection sizes are known for only some of the subfamilies, or when these quantities
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Estimating the number of clusters in a dataset via the Gap statistic
, 2000
"... We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference ..."
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Cited by 492 (1 self)
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We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference
InclusionExclusion Algorithms for Counting Set Partitions
, 2006
"... Given an nelement set U and a family of subsets S ⊆ 2 U we show how to count the number of kpartitions S1 ∪ · · · ∪ Sk = U into subsets Si ∈ S in time 2 n n O(1). The only assumption on S is that it can be enumerated in time 2 n n O(1). In effect we get exact algorithms in time 2 n n O(1) fo ..."
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Cited by 36 (1 self)
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Given an nelement set U and a family of subsets S ⊆ 2 U we show how to count the number of kpartitions S1 ∪ · · · ∪ Sk = U into subsets Si ∈ S in time 2 n n O(1). The only assumption on S is that it can be enumerated in time 2 n n O(1). In effect we get exact algorithms in time 2 n n O(1
Mediators in the architecture of future information systems
 IEEE COMPUTER
, 1992
"... The installation of highspeed networks using optical fiber and high bandwidth messsage forwarding gateways is changing the physical capabilities of information systems. These capabilities must be complemented with corresponding software systems advances to obtain a real benefit. Without smart softw ..."
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Cited by 1128 (20 self)
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level functional partitioning. These partitions are mapped into information processing modules. The modules are assigned to nodes of the distributed information systems. A central role is assigned to modules that mediate between the users ' workstations and data resources. Mediators contain
Results 1  10
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611,618