Let G = (V, E) be a directed graph, and let w, be the weight of vertex v for every v € V. We say that a directed edge e = (u, v) is d-covered by a multi-set (a set that can contain elements more than one time) of vertices S if either u is in S at least once, or v is in S at least twice. The weight of a multi-set of vertices S is the sum of the weights of the vertices (where vertices that appear more than once, appear in the sum more than once). 1. Write an IP that finds the multi-set S that d-cover all edges, and minimizes the weight. 2. Write an LP that relaxes the IP. 3. Describe a rounding scheme that guarantees a 2-approximation to the best multi-set.
Let G = (V, E) be a directed graph, and let w, be the weight of vertex v for every v € V. We say that a directed edge e = (u, v) is d-covered by a multi-set (a set that can contain elements more than one time) of vertices S if either u is in S at least once, or v is in S at least twice. The weight of a multi-set of vertices S is the sum of the weights of the vertices (where vertices that appear more than once, appear in the sum more than once). 1. Write an IP that finds the multi-set S that d-cover all edges, and minimizes the weight. 2. Write an LP that relaxes the IP. 3. Describe a rounding scheme that guarantees a 2-approximation to the best multi-set.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Transcribed Image Text:Let G = (V, E) be a directed graph, and let w, be the weight of vertex v for every v € V. We say that a directed edge
e = (u, v) is d-covered by a multi-set (a set that can contain elements more than one time) of vertices S if either u is
in S at least once, or v is in S at least twice. The weight of a multi-set of vertices S is the sum of the weights of the
vertices (where vertices that appear more than once, appear in the sum more than once).
1. Write an IP that finds the multi-set S that d-cover all edges, and minimizes the weight.
2. Write an LP that relaxes the IP.
3. Describe a rounding scheme that guarantees a 2-approximation to the best multi-set.
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