Related papers: About Testing the Speed of Calculating the Shortes…
Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal…
The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
In this paper we develop two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty. First, we extend an algorithm of Bertsimas and Sim (2003)…
We study the problem of computing constrained shortest paths for battery electric vehicles. Since battery capacities are limited, fastest routes are often infeasible. Instead, users are interested in fast routes on which the energy…
The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversal-based approximation algorithm for this problem…
Statistical static timing analysis (SSTA) is studied from the point of view of mathematical optimization. We present two formulations of the problem of finding the critical path delay distribution that were not known before: (i) a…
In this paper we initiate the study of the temporal graph realization problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an $n \times n$ matrix $D$ and a $\Delta \in…
Due to the computational complexity of finding almost shortest simple paths, we propose that identifying a larger collection of (nonbacktracking) paths is more efficient than finding almost shortest simple paths on positively weighted…
We describe a general purpose algorithm for counting simple cycles and simple paths of any length $\ell$ on a (weighted di)graph on $N$ vertices and $M$ edges, achieving a time complexity of $O\left(N+M+\big(\ell^\omega+\ell\Delta\big)…
We present the quantum algorithm for the Longest Trail Problem. The problem is to search the longest edge-simple path for a graph with $n$ vertexes and $m$ edges. Here edge-simple means no edge occurs in the path twice, but vertexes can…
Automated driving in urban scenarios requires efficient planning algorithms able to handle complex situations in real-time. A popular approach is to use graph-based planning methods in order to obtain a rough trajectory which is…
The traditional complex network approach considers only the shortest paths from one node to another, not taking into account several other possible paths. This limitation is significant, for example, in urban mobility studies. In this short…
The trapping problem on graph (or network) as a typical focus of great interest has attracted more attention from various science fields, including applied mathematics and theoretical computer science, in the past. Here, we first study this…
Fastest-path queries between two points in a very large road map is an increasingly important primitive in modern transportation and navigation systems, thus very efficient computation of these paths is critical for system performance and…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
We develop an efficient parallel algorithm for answering shortest-path queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small…
In [1], a new construction called red-black hierarchy characterizing Laman graphs and an algorithm for computing it were presented. For a Laman graph G=(V,E) with n vertices it runs in O(n^2) time assuming that a partition of (V,E+e) into…
Consider a general path planning problem of a robot on a graph with edge costs, and where each node has a Boolean value of success or failure (with respect to some task) with a given probability. The objective is to plan a path for the…