7.1 Multicut
نویسندگان
چکیده
P∈Pi P∋e fi,P ≤ ce ∀e fi,P ≥ 0 Dual 1 solves the max-sum multi-commodity flow problem: ce represents the capacity of an edge, and fi,P is the amount of flow directed from si to ti along the path P . The LP tries to maximize the total amount of commodity flow. Lemma 17.1.1 Multicut is always larger than the corresponding max-sum multi-commodity flow. Lemma 17.1.2 Multicut is at most O(logK) times the corresponding max-sum multi-commodity flow. Theorem 17.1.3 When k = 2, multicut equals max-sum multi-commodity flow.
منابع مشابه
Approximation Algorithms Fall Semester , 2003 Lecture 7 : Sept 22 , 2003
1 Multicut We will now study an example of randomized rounding, where the geometry of the solution space is used in constructing the approximation algorithm. The multicut probem has as input an undirected graph G = (V,E), nonnegative costs associated with each edge (i.e. c : E → Q) and k terminal pairs (s1, t1), (s2, t2), . . ., (sk, tk). A multicut is a subset of edges, F , such that removing ...
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