# Instance Class BoundedSpanningTree

Class Tree [Root]    Unclassified (3031) Let G be a *directed* graph. A spanning tree is d-bounded if for every vertex the number of outgoing edges at this vertex is at most d. In the bounded spanning tree problem we are given a directed graph G=(V,E), where V is the set of vertices and E is the set of edges. We are also given a bound d. The goal is to find a d-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 is the single line: bound(d). 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). bound(1). Output Requirement ================== The solution must be encoded by a binary predicate "bstedge", where "bstedge(i,j)" stands for: "edge(i,j) of G is in the bounded spanning tree". For the input given above, the following is a 1-bounded spanning tree: bstedge(1,2) bstedge(2,3) bstedge(3,4) The corresponding answer set produced by a solver must contain exactly these ground atoms of the form "bstedge" (and possibly some other atoms based on other predicates). For the same input, the following *is not* a 1-bounded spanning tree (even though it is a spanning tree): bstedge(1,2) bstedge(2,3) bstedge(2,4) Authors: Gayathri Namasivayam and Miroslaw Truszczynski Affiliation: University of Kentucky Email: {gayathri, mirek}@cs.uky.edu Martin Gebser 122_rand_35_250_1700138821_0     122_rand_35_250_1700139696_0     122_rand_35_250_1700139777_0     122_rand_35_250_1700159740_0     122_rand_35_250_1700163981_0     122_rand_35_250_1700164334_0     122_rand_35_250_1700164416_0     122_rand_35_250_1700165461_0     122_rand_35_250_1700167407_0     122_rand_35_250_1700167469_0    un-/mark all