2000
DOI: 10.1007/s004530010013
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Approximation Algorithms for Minimum K -Cut

Abstract: Let G = (V, E) be a complete undirected graph, with node set V = {v 1 , . . . , v n } and edge set E. The edges (v i , v j ) ∈ E have nonnegative weights that satisfy the triangle inequality. Given a set of integers, minimizing the total weight of edges whose two ends are in different subsets. We demonstrate that for any fixed p it is possible to obtain in polynomial time an approximation of at most three times the optimal value. We also prove bounds on the ratio between the weights of maximum and minimum cuts. Show more

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Cited by 25 publications
(24 citation statements)
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“…Hence the overall asymptotic complexity of Min-Star-Partition is O(n x+1 ) time, which is polynomial when x is a constant. Please refer [17] for further details.…”
Section: Algorithm 3 Algorithm Min-star-partitionmentioning
confidence: 99%
See 1 more Smart Citation
“…Hence the overall asymptotic complexity of Min-Star-Partition is O(n x+1 ) time, which is polynomial when x is a constant. Please refer [17] for further details.…”
Section: Algorithm 3 Algorithm Min-star-partitionmentioning
confidence: 99%
“…The proof uses an easy reduction from [17]. We start by showing how the solution to SpltBOpt problem could be bounded by the solution of a slightly different problem variant, known as Min-Star problem [17].…”
Section: Algorithm 3 Algorithm Min-star-partitionmentioning
confidence: 99%
“…By the analysis of T. Tokuyama [13], the min-star problem can be solved in O(n). According to [14], the following result shows the connection between the min-star problem and Problem 5. Lemma 4 implies that suppose one of the terminal sets of the optimal partition is known to us, we have already had an efficient approximation algorithm for the equal-sized community detection problem.…”
Section: Problem 4 Equal-sized Community Detection Problemmentioning
confidence: 99%
“…Even though the number of subgroups (aka partitions) is n K with K workers in all but last subgroup, finding an optimal assignment of the n workers across those subgroups that minimizes the objective function is NP-hard. The proof uses an easy reduction from [20]. We start by showing how the solution to SpltBOpt problem could be bounded by the solution of a slightly different problem variant, known as Min-Star problem [20].…”
Section: α# ####################α# A# C# D# E# ####################αmentioning
confidence: 99%