Complexity of network synchronization
Journal of the ACM (JACM)
There are planar graphs almost as good as the complete graph
Journal of Computer and System Sciences
An optimal synchronizer for the hypercube
SIAM Journal on Computing
NP-completeness of minimum spanner problems
Discrete Applied Mathematics
On the minimum diameter spanning tree problem
Information Processing Letters
Tree spanners in planar graphs
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Some optimal inapproximability results
Journal of the ACM (JACM)
Distance Approximating Spanning Trees
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
MAD Trees and distance-hereditary graphs
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
SIAM Journal on Discrete Mathematics
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
Hi-index | 5.23 |
We draw attention to combinatorial network abstraction problems. These are specified by a class P of pattern graphs and a real-valued similarity measure @r that is based on certain graph properties. For a fixed pattern P and similarity measure @r, the optimization task on a given graph G is to find a subgraph G^'@?G which belongs to P and minimizes @r(G,G^'). In this work, we consider this problem for the natural and somewhat general case of trees and distance-based similarity measures. In particular, we systematically study spanning trees of graphs that minimize distances, approximate distances, and approximate closeness-centrality with respect to standard vector- and matrix-norms. Complexity analysis within a unifying framework shows that all considered variants of the problem are NP-complete, except for the case of distance-minimization with respect to the norm L"~. If a subset of edges can be ''forced'' into the spanning tree, no polynomial-time constant-factor approximation algorithmexists for the distance-approximation problems unless P=NP.