Related papers: Interchanging distance and capacity in probabilist…
In this paper we provide a method of finding possible numbers of shortest paths between two points in a space of compact sets in Euclidean space with Hausdorff distance. We also prove that there cannot be some of the numbers of shortest…
In a 1989 paper titled "shortest paths without a map", Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph for a target node, while attempting to minimize the total length of the path traversed…
We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…
We study a scenario for route planning in road networks, where the objective to be optimized may change between every shortest path query. Since this invalidates many of the known speedup techniques for road networks that are based on…
Computing a minimum path cover (MPC) of a directed acyclic graph (DAG) is a fundamental problem with a myriad of applications, including reachability. Although it is known how to solve the problem by a simple reduction to minimum flow,…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by…
In this paper we introduce and study the Minimum Edge Compact Spanner~(MECS) problem. We prove hardness results related to the problem, design exact and greedy algorithms for solving the problem, and show related experimental results. The…
Identifying shortest paths between nodes in a network is a common graph analysis problem that is important for many applications involving routing of resources. An adversary that can manipulate the graph structure could alter traffic…
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
In a dense Low Earth Orbit (LEO) satellite constellation, using a centralized algorithm for minimum-delay routing would incur significant signaling and computational overhead. In this work, we exploit the deterministic topology of the…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
In this invited contribution, we revisit the stochastic shortest path problem, and show how recent results allow one to improve over the classical solutions: we present algorithms to synthesize strategies with multiple guarantees on the…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
We present Roadmap Sparsification by Edge Contraction (RSEC), a simple and effective algorithm for reducing the size of a motion-planning roadmap. The algorithm exhibits minimal effect on the quality of paths that can be extracted from the…
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for…
We show an improved parallel algorithm for decomposing an undirected unweighted graph into small diameter pieces with a small fraction of the edges in between. These decompositions form critical subroutines in a number of graph algorithms.…
In this paper we introduce min-plus low rank matrix approximation. By using min and plus rather than plus and times as the basic operations in the matrix multiplication; min-plus low rank matrix approximation is able to detect…
A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…