We present a fast algorithm for uniform sampling of contiguous minimum cuts separating a source vertex from a set of sink vertices in a weighted undirected planar graph with n vertices embedded in the plane. The algorithm takes O(n) time per sample, after an initial O(n) preprocessing time during which the algorithm computes the number of all such contiguous minimum cuts. Contiguous cuts (that ...

The resonance graph of a benzenoid graph G has the 1-factors of G as vertices, two 1-factors being adjacent if their symmetric difference forms the edge set of a hexagon of G. It is proved that the smallest number of elementary cuts that cover a catacondensed benzenoid graph equals the dimension of a largest induced hypercube of its resonance graph.

We study solution approaches for the design of reliably connected networks. Specifically, given a network with arcs that may fail at random, the goal is to select a minimum cost subset of arcs such the probability that a connectivity requirement is satisfied is at least 1− , where is a risk tolerance. We consider two types of connectivity requirements. We first study the problem of requiring an...

We present an Õ(m) (near-linear) time Monte Carlo algorithm for constructing the cactus data structure, a useful representation of all the global minimum edge cuts of an undirected graph. Our algorithm represents a fundamental improvement over the best previous (quadratic time) algorithms: because there can be quadratically many min-cuts, our algorithm must avoid looking at all min-cuts during ...

Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG) framework, we represent RNA...

We improve on random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time construction that transforms any graph on vertices into an -edge graph on the same vertices whose cuts have approximately the same value as the original graph’s. In this new graph, for example, we can run the
-time maximum flow algorithm of Goldberg and...

Many graph-based learning problems can be cast as finding a good set of vertices nearby a seed set, and a powerful methodology for these problems is based on maximum flows. We introduce and analyze a new method for locally-biased graphbased learning called SimpleLocal, which finds good conductance cuts near a set of seed vertices. An important feature of our algorithm is that it is strongly-loc...

Automatic segmentation of the left atrium (LA) with the left atrial appendage (LAA) and the pulmonary vein (PV) trunks is important for intra-operative guidance in radio-frequency catheter ablation to treat atrial fibrillation (AF). Recently, we proposed a model-based method for LA segmentation from the C-arm CT images using marginal space learning (MSL). However, on some data, the mesh from th...

We present a graph cuts-based image segmentation technique that incorporates an elliptical shape prior. Inclusion of this shape constraint restricts the solution space of the segmentation result, increasing robustness to misleading information that results from noise, weak boundaries, and clutter. We argue that combining a shape prior with a graph cuts method suggests an iterative approach that...

We present a framework for object segmentation using depth maps based on Random Forest and Graph-cuts theory, and apply it to the segmentation of human limbs. First, from a set of random depth features, Random Forest is used to infer a set of label probabilities for each data sample. This vector of probabilities is used as unary term in α − β swap Graph-cuts algorithm. Moreover, depth values of...