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Enabling robots to perform complex dynamic tasks such as picking up an object in one sweeping motion or pushing off a wall to quickly turn a corner is a challenging problem. The dynamic interactions implicit in these tasks are critical…
This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems…
Highly dynamic networks rarely offer end-to-end connectivity at a given time. Yet, connectivity in these networks can be established over time and space, based on temporal analogues of multi-hop paths (also called {\em journeys}).…
The quest for optimal/stable paths in graphs has gained attention in a few practical or theoretical areas. To take part in this quest this chapter adopts an equilibrium-oriented approach that is abstract and general: it works with…
Real-time navigation in dense human environments is a challenging problem in robotics. Most existing path planners fail to account for the dynamics of pedestrians because introducing time as an additional dimension in search space is…
Modeling and simulation of pedestrian behavior is used in applications such as planning large buildings, disaster management, or urban planning. Realistically simulating pedestrian behavior is challenging, due to the complexity of…
In this paper, we introduced a novel approach to computing the fewest-turn map directions or routes based on the concept of natural roads. Natural roads are joined road segments that perceptually constitute good continuity. This approach…
We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…
This paper presents a review for the development of Intelligent Transportation System (ITS) world wide and the use of Smart Antennas in ITS. This review work also discusses the usual problems in ITS and proposes the solution of such…
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…
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…
In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are…
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…
Graphs of Convex Sets (GCS) is a recent method for synthesizing smooth trajectories by decomposing the planning space into convex sets, forming a graph to encode the adjacency relationships within the decomposition, and then simultaneously…
Factor graphs are graphical models used to represent a wide variety of problems across robotics, such as Structure from Motion (SfM), Simultaneous Localization and Mapping (SLAM) and calibration. Typically, at their core, they have an…
For automotive applications, the Graph Attention Network (GAT) is a prominently used architecture to include relational information of a traffic scenario during feature embedding. As shown in this work, however, one of the most popular GAT…
Graph algorithms enormously contribute to the domains such as blockchains, social networks, biological networks, telecommunication networks, and several others. The ever-increasing demand of data-volume, as well as speed of such…
We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms of tropical geometry. Applications include shortest paths in traffic networks with variable link travel times.
In the graph exploration problem, a team of mobile computational entities, called agents, arbitrarily positioned at some nodes of a graph, must cooperate so that each node is eventually visited by at least one agent. In the literature, the…
Routing strategies for traffics and vehicles have been historically studied. However, in the absence of considering drivers' preferences, current route planning algorithms are developed under ideal situations where all drivers are expected…