Name
Abstract | ||
|---|---|---|
Given a d-regular bipartite graph Gd, whose nodes are divided in black nodes and white nodes according to the partition, we consider the problem of computing the spanning tree of Gd with the maximum number of black leaves. We prove that the problem is NP hard for any fixed d ≥ 4 and we present a simple greedy algorithm that gives a constant approximation ratio for the problem. More precisely our algorithm can be used to get in linear time an approximation ratio of 2 - 2/(d - 1)2 for d ≥ 4. When applied to cubic bipartite graphs the algorithm only achieves a 2-approximation ratio. Hence we introduce a local optimization step that allows us to improve the approximation ratio for cubic bipartite graphs to 1.5. Focusing on structural properties, the analysis of our algorithm proves a lower bound on lB(n, d), i.e., the minimum m such that every Gd with n black nodes has a spanning tree with at least m black leaves. In particular, for d = 3 we prove that lB(n, 3) is exactly ⌈n/3⌉ +1. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/978-3-540-77120-3_78 | ISAAC |
Keywords | Field | DocType |
constant approximation ratio,approximation ratio,simple greedy algorithm,m black leave,black leave,cubic bipartite graph,d-regular bipartite graph,spanning tree,n black node,black node,2-approximation ratio,linear time,greedy algorithm,bipartite graph,lower bound | Discrete mathematics,Complete bipartite graph,Combinatorics,Minimum degree spanning tree,Distributed minimum spanning tree,Bipartite graph,Spanning tree,Reverse-delete algorithm,Mathematics,Kruskal's algorithm,Minimum spanning tree | Conference |
ISBN | Citations | PageRank |
3-540-77118-2 | 0 | 0.34 |
References | Authors | |
16 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Emanuele G. Fusco | 1 | 86 | 9.03 |
| Angelo Monti | 2 | 671 | 46.93 |