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Sampling-based motion planning techniques have emerged as an efficient algorithmic paradigm for solving complex motion planning problems. These approaches use a set of probing samples to construct an implicit graph representation of the…

Motion planning in modified environments is a challenging task, as it compounds the innate difficulty of the motion planning problem with a changing environment. This renders some algorithmic methods such as probabilistic roadmaps less…

MapReduce is becoming the de facto framework for storing and processing massive data, due to its excellent scalability, reliability, and elasticity. In many MapReduce applications, obtaining a compact accurate summary of data is essential.…

A robust, resource-efficient, distributed, and minimally parameterized 3D map matching and merging algorithm is proposed. The suggested algorithm utilizes tomographic features from 2D projections of horizontal cross-sections of…

Humans can learn concepts or recognize items from just a handful of examples, while machines require many more samples to perform the same task. In this paper, we build a computational model to investigate the possibility of this kind of…

Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…

Images have become an important data source in many scientific and commercial domains. Analysis and exploration of image collections often requires the retrieval of the best subregions matching a given query. The support of such…

We introduce in this paper a new summarization method for large graphs. Our summarization approach retains only a user-specified proportion of the neighbors of each node in the graph. Our main aim is to simplify large graphs so that they…

When creating choropleth maps, mapmakers often bin (i.e., group, classify) quantitative data values into groups to help show that certain areas fall within a similar range of values. For instance, a mapmaker may divide counties into groups…

Self-organizing maps (SOMs) are a technique that has been used with high-dimensional data vectors to develop an archetypal set of states (nodes) that span, in some sense, the high-dimensional space. Noteworthy applications include weather…

A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…

Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include…

Many real-world datasets can be naturally represented as graphs, spanning a wide range of domains. However, the increasing complexity and size of graph datasets present significant challenges for analysis and computation. In response, graph…

We consider the problem of resolving closely spaced point sources in one dimension from their Fourier data in a bounded domain. Classical subspace methods (e.g., MUSIC algorithm, Matrix Pencil method, etc.) show great superiority in…

Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…

Points of interest on a map such as restaurants, hotels, or subway stations, give rise to categorical point data: data that have a fixed location and one or more categorical attributes. Consequently, recent years have seen various set…

Maps provide robots with crucial environmental knowledge, thereby enabling them to perform interactive tasks effectively. Easily accessing accurate abstract-to-detailed geometric and semantic concepts from maps is crucial for robots to make…

Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible…

3D scene graphs hierarchically represent the environment appropriately organizing different environmental entities in various layers. Our previous work on situational graphs extends the concept of 3D scene graph to SLAM by tightly coupling…

Current applications have produced graphs on the order of hundreds of thousands of nodes and millions of edges. To take advantage of such graphs, one must be able to find patterns, outliers and communities. These tasks are better performed…