Class Tree  

Description 
Let G be a *directed* graph. Let every edge in the graph be assigned a weight. A spanning tree is wbounded if for every vertex the sum of the weights of the outgoing edges at this vertex is atmost w. In the weighted spanning tree problem we are given a directed graph G=(V,E,W), where V is the set of vertices, E is the set of edges and W is a function that maps each edge in the graph to an integer weight from the range 1..V. We are also given an integer bound w. The goal is to find a wbounded spanning tree in G. Input Format ============ Input data are stored in a plain text file. The format of the file is as follows: a. The file starts with n lines that define the number of vertices in the problem using predicate "vtx" as follows. vtx(1). vtx(2). ... vtx(n). b. The file then specifies the edges of the graph using predicate "edge". Each line is of the form "edge(i,j)", meaning that there is a directed edge from vertex i to vertex j. c. Then there are as many lines as there are edges in the graph of the form Weight wtedge(i,j)=v. c. Then there is the single line bound(w). Example input: vtx(1). vtx(2). vtx(3). vtx(4). edge(1,2). edge(2,3). edge(2,4). edge(3,4). edge(1,4). Weight wtedge(1,2)=1. Weight wtedge(2,3)=2. Weight wtedge(2,4)=1. Weight wtedge(3,4)=2. Weight wtedge(1,4)=1. bound(2). Output Requirement ================== The solution must be encoded by a binary predicate "wstedge", where "wstedge(i,j)" stands for: "there is an edge(i,j) in the weighted spanning tree". For the input given above, the following is a 2weighted spanning tree: wstedge(1,2) wstedge(2,3) wstedge(3,4) The corresponding answer set produced by a solver must contain exactly these ground atoms of the form "wstedge" (and possibly some other atoms based on other predicates). For the same input, the following *is not* a 2weighted spanning tree: wstesge(1,2) wstedge(2,3) wstedge(2,4) Authors: Gayathri Namasivayam and Miroslaw Truszczynski Affiliation: University of Kentucky Email: {gayathri, mirek}@cs.uky.edu 
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