Related papers: Graph traversals associated with iterative methods…
Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…
This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing…
Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with…
Distributed processing of large-scale graph data has many practical applications and has been widely studied. In recent years, a lot of distributed graph processing frameworks and algorithms have been proposed. While many efforts have been…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on…
Graph drawing addresses the problem of finding a layout of a graph that satisfies given aesthetic and understandability objectives. The most important objective in graph drawing is minimization of the number of crossings in the drawing, as…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…
Data-intensive, graph-based computations are pervasive in several scientific applications, and are known to to be quite challenging to implement on distributed memory systems. In this work, we explore the design space of parallel algorithms…
Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…
Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…
We study distributed graph algorithms that adopt an iterative vertex-centric framework for graph processing, popularized by the Google's Pregel system. Since then, there are several attempts to implement many graph algorithms in a…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
This research considers Bayesian decision-analytic approaches toward the traversal of an uncertain graph. Namely, a traveler progresses over a graph in which rewards are gained upon a node's first visit and costs are incurred for every edge…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…
In this paper we show how to combine two algorithmic techniques to obtain linear time algorithms for various optimization problems on graphs, and present a subroutine which will be useful in doing so. The first technique is iterative…
We survey graph reachability indexing techniques for efficient processing of graph reachability queries in two types of popular graph models: plain graphs and edge-labeled graphs. Reachability queries are Boolean in nature, determining…