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cs500_sol1 - S500 Algorithms Homework#1 Solution 1(1 False...

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S500 Algorithms Homework #1 Solution 1. (1) False (2) False 2. Reduce the problem into a max-flow problem. z Construct flow network by given parameters. (see the above example) z Run max-flow algorithm on the constructed network. z If |f| is equal to the number of client, conclude that every client can be connected simultaneously to a base station. 1 L L 1 1 1 L s C 1 B 2 B 1 t B 3 Base C 2 Client 1 1 E = {(s, C i ) : C i ∈ Client} ∪ {(C i , B j ) : C i ∈ Client, B j ∈ Base and dist(C i , B j ) < r} ∪ {(B i , t) : B i ∈ Base} 1/1 1/2 1/2 1/1 3/4 1/1 1/2 s t 2/2 2/3 2/3 1/2 5/5 2/2 1/3 s t s 1/2 1/1 t
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3. The edge connectivity z Algorithm Construct flow network; directed graph G’=(V’, E’) by given undirected graph G=(V, E) such that V’ = V and E’ = {(u i , v i ), (v i , u i ) : e i =(u i , v i )∈E} with each edge capacity 1 Choose a vertex u as source Define |f uv | as maximum flow of G’ with source u and sink v Min{|f uv | : v ∈V-{u} } z Analysis The number of flow networks is |V|-1 The number of vertices is O(V) The number of vertices is O(E) 4. a. Separate the vertex into two pieces.
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