NDLI: Approximating k-cuts via network strength

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Approximating k-cuts via network strength

Content Provider	ACM Digital Library
Author	Sinha, Amitabh Ravi, R.
Abstract	Let G = (V, E) be an undirected connected graph with edge weights s: E → $IR^{+}.$ An edge set A ⊆ E is called a k-cut if G′ = (V,E\A) has k connected components. The k-cut problem is to compute a minimum weight k-cut in G.The k-cut problem is known to be NP-hard. Saran and Vazirani [3] gave a combinatorial (2-2/k)-approximation which successively finds minimum cuts until the graph is partitioned into k components. Recently, Naor and Rabani [2] gave an integer program formulation of the problem, and showed that its integrality gap is 2.1.1 Our Contributions. We provide a new combinatorial polynomial-time approximation algorithm to the k-cut problem, with worst-case performance ratio 2. We also provide a new combinatorial lower bound, which is provably at least as good as the Naor-Rabani LP lower bound.1.2 Network Strength and Attack. For an edge set A, let k (A) denote the number of connected components in G′ = (V,E\A). Define s(A) = $∑_{eεA}$ s (e). The strength of the edge set A is defined to be σ(A) := s(A)/(k(A) - 1), and the strength of the graph G is σ(G) $:=min_{A⊆Eσ}(A).$ The strength of a singleton node is defined to be infinity.For an edge set A and a real number b > 0, define gA(b) := s(A) - b(k(A) - 1). Let g(b) := minA⊆EgA(b) be the attack value of the network. We use e(b) to denote the edge set which achieves this minimum. Define k(b) := k(e(b)). Note that g(b) is always non-positive, since letting A = Ø achieves g(b) = O.Cunningham [1] provided polynomial-time algorithms to compute both the strength and the attack value of a network. We use Cunningham's algorithms as a subroutine in our algorithm.
Starting Page	621
Ending Page	622
Page Count	2
File Format	PDF
ISBN	089871513X
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2002-01-06
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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