Distributed Approximation Algorithms for Weighted Problems in Minor-Closed Families

Distributed algorithms for weighted problems in minor-closed families

We give efficient distributed algorithms for weighted versions of the maximum matching problem and the minimum dominating set problem for graphs from minor-closed families. To complement these results we argue that no efficient distributed algorithm for the minimum weight connected dominating set exists.

Node-Weighted Network Design in Planar and Minor-Closed Families of Graphs

We consider node-weighted network design in planar and minor-closed families of graphs. In particular we focus on the edge-connectivity survivable network design problem (EC-SNDP). The input consists of a node-weighted undirected graph G = (V,E) and integral connectivity requirements r(uv) for each pair of nodes uv. The goal is to find a minimum node-weighted subgraph H of G such that, for each...

Distributed Almost Exact Approximations for Minor-Closed Families

We give efficient deterministic distributed algorithms which given a graph G from a proper minor-closed family C find an approximation of a minimum dominating set in G and a minimum connected dominating set in G. The algorithms are deterministic and run in a polylogarithmic number of rounds. The approximation accomplished differs from an optimal by a multiplicative factor of (1 + o(1)).

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Approximation Algorithms via Contraction DecompositionA preliminary version of this paper appears in Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, January 2007

We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number k of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound depends on k). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained in [Bak94, Epp00, DDO04, DHK05], and it generalizes a...