Name
Abstract | ||
|---|---|---|
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a key role in, e.g., network reliability under random edge failure, estimation over networks and D-optimal experimental designs. This paper tackles the open problem of designing graphs with the maximum weighted number of spanning trees under various constraints. We reveal several new structures, such as the log-submodularity of the weighted number of spanning trees in connected graphs. We then exploit these structures and design a pair of efficient approximation algorithms with performance guarantees and near-optimality certificates. Our results can be readily applied to a wide verity of applications involving graph synthesis and graph sparsification scenarios. |
Year | Venue | Field |
|---|---|---|
2016 | arXiv: Data Structures and Algorithms | Discrete mathematics,Approximation algorithm,Trémaux tree,Indifference graph,Combinatorics,Minimum degree spanning tree,Open problem,Spanning tree,Reliability (computer networking),Pathwidth,Mathematics |
DocType | Volume | Citations |
Journal | abs/1604.01116 | 1 |
PageRank | References | Authors |
0.48 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kasra Khosoussi | 1 | 32 | 6.15 |
| Gaurav S. Sukhatme | 2 | 5469 | 548.13 |
| Shoudong Huang | 3 | 755 | 62.77 |
| Gamini Dissanayake | 4 | 2226 | 256.36 |