Absfmcf-We consider the real-weight maximum cut of a planar graph. Given an undirected planar graph with real-valued weights associated with its edges, find a partition of the vertices into two nonemply sets such that the sum of the weights of the edges connecting the two sets is maximum. The conventional maximum cut and minimum cut problems assume nonnegative edge weights, and thus are special...

Recently, unsupervised image segmentation has become increasingly popular. Starting from a superpixel segmentation, an edge-weighted region adjacency graph is constructed. Amongst all segmentations of the graph, the one which best conforms to the given image evidence, as measured by the sum of cut edge weights, is chosen. Since this problem is NP-hard, we propose a new approximate solver based ...

The LM-Cut planner uses the landmark-cut heuristic, introduced by the authors in 2009, within a standard A∗ progression search framework to find optimal sequential plans for STRIPS-style planning tasks. This short paper recapitulates the main ideas surrounding the landmark-cut heuristic and provides pointers for further reading.

Partitioning of a graph representation, defined over low-level image features based on Gestalt inspired relations, is an effective strategy for forming coherent perceptual groups in an image. The usual practice, mainly motivated by efficiency considerations, is to approximate the general K-way partitioning solution by recursive bi-partitioning, where at each step the graph is broken into two pa...

Branch-and-cut methods are exact algorithms for integer programming problems. They consist of a combination of a cutting plane method with a branch-and-bound algorithm. These methods work by solving a sequence of linear programming relaxations of the integer programming problem. Cutting plane methods improve the relaxation of the problem to more closely approximate the integer programming probl...

An odd hole is an induced odd cycle of length at least 5. Scott and Seymour confirmed a conjecture of Gyárfás and proved that if a graph G has no odd holes then χ(G) 6 22 ω(G)+2 . Chudnovsky, Robertson, Seymour and Thomas showed that if G has neither K4 nor odd holes then χ(G) 6 4. In this note, we show that if a graph G has neither triangles nor quadrilaterals, and has no odd holes of length a...