Glencora Borradaile

An O ( n log n ) approximation scheme for Steiner tree in planar graphs

We give a Polynomial-Time Approximation Scheme (PTAS) for the Steiner tree problem in planar graphs. The running time is <i>O</i>(<i>n</i> log <i>n</i>).

An O ( n log n ) algorithm for maximum st -flow in a directed planar graph

We give the first correct <i>O</i>(<i>n</i> log <i>n</i>) algorithm for finding a maximum <i>st</i>-flow in a directed planar graph. After a preprocessing step that consists in finding single-source shortest-path distances in the dual, the algorithm consists of repeatedly saturating the leftmost residual <i>s</i>-to-<i>t</i> path.

An O (n log n) algorithm for maximum st -flow in a directed planar graph

We give the first correct O(n log n) algorithm for finding a maximum st-flow in a directed planar graph. After a preprocessing step that consists in finding single-source shortest-path distances in the dual, the algorithm consists of repeatedly saturating the leftmost residual s-to-t path.

Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs

We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded-genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The schemes run in

Multiple-Source Multiple-Sink Maximum Flow in Directed Planar Graphs in Near-Linear Time

\mathcal{O}(n \log n)

Min st -Cut Oracle for Planar Graphs with Near-Linear Preprocessing Time

time for graphs embedded on both orientable and nonorientable surfaces. This work generalizes the PTAS framework from planar graphs to bounded-genus graphs: any problem that is shown to be approximable by the planar PTAS framework of Borradaile et al. (ACM Trans. Algorithms 5(3), 2009) will also be approximable in bounded-genus graphs by our extension.

Steiner tree in planar graphs: an O ( n log n ) approximation scheme with singly-exponential dependence on epsilon

We give an O(n log3 n) algorithm that, given an n-node directed planar graph with arc capacities, a set of source nodes, and a set of sink nodes, finds a maximum flow from the sources to the sinks. Previously, the fastest algorithms known for this problem were those for general graphs.

A Polynomial-Time Approximation Scheme for Euclidean Steiner Forest

For an undirected

Safe and tight linear estimators for global optimization

n

The Two-Edge Connectivity Survivable-Network Design Problem in Planar Graphs

-vertex planar graph