Related papers: A $k$-medoids Approach to Exploring Districting Pl…
We introduce a graph-theoretic framework based on discrete sheaves to diagnose and localize inconsistencies in preference aggregation. Unlike traditional linearization methods (e.g., HodgeRank), this approach preserves the discrete…
We consider the problem of characterizing graphs with the maximum spectral radius among the connected graphs with given numbers of vertices and edges. It is well-known that the candidates for extremal graphs are threshold graphs, but only a…
Partitioning a graph into balanced components is important for several applications. For multi-objective problems, it is useful not only to find one solution but also to enumerate all the solutions with good values of objectives. However,…
The $k$-segmentation of a video stream is used to partition it into $k$ piecewise-linear segments, so that each linear segment has a meaningful interpretation. Such segmentation may be used to summarize large videos using a small set of…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
We provide a rearrangement based algorithm for fast detection of subgraphs of $k$ vertices with long escape times for directed or undirected networks. Complementing other notions of densest subgraphs and graph cuts, our method is based on…
A distributed algorithm performs local computations on pieces of input and communicates the results through given communication links. When processing a massive graph in a distributed algorithm, local outputs must be configured as a…
Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on…
The watershed is a powerful tool for segmenting objects whose contours appear as crest lines on a gradient image. The watershed transform associates to a topographic surface a partition into catchment basins, defined as attraction zones of…
This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…
We propose Distributed Neighbor Expansion (Distributed NE), a parallel and distributed graph partitioning method that can scale to trillion-edge graphs while providing high partitioning quality. Distributed NE is based on a new heuristic,…
Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
Purpose: To improve kidney segmentation in clinical ultrasound (US) images, we develop a new graph cuts based method to segment kidney US images by integrating original image intensity information and texture feature maps extracted using…
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the…
We study the k-median and k-center problems in probabilistic graphs. We analyze the hardness of these problems, and propose several algorithms with improved approximation ratios compared with the existing proposals.
Partisan gerrymandering is a major cause for voter disenfranchisement in United States. However, convincing US courts to adopt specific measures to quantify gerrymandering has been of limited success to date. Recently, Stephanopoulos and…
We present algorithms and experiments for the visualization of directed graphs that focus on displaying their reachability information. Our algorithms are based on the concepts of the path and channel decomposition as proposed in the…