# Instance Class WeightedSpanningTree

Class Tree Let G be a *directed* graph. Let every edge in the graph be assigned a weight. A spanning tree is w-bounded 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 w-bounded 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 2-weighted 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 2-weighted 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 Martin Gebser 207_rand_35_138_2077106370_0     207_rand_35_138_2077111672_0     207_rand_35_138_2077113361_0     207_rand_35_138_2077119725_0     207_rand_35_138_2077159055_0     209_rand_45_138_1119566765_0     209_rand_45_138_1119566817_0     209_rand_45_138_1119567351_0     209_rand_45_138_1119569108_0     209_rand_45_138_1119571853_0    un-/mark all