Related papers: Faster All-Pairs Optimal Electric Car Routing
Given a graph $G=(V,E)$ and two vertices $s,t\in V$, the $f$-fault replacement path ($f$FRP) problem computes for every set of edges $F$ where $|F|\leq f$, the distance from $s$ to $t$ when edges in $F$ fail. A recent result shows that 2FRP…
The all pairs shortest path problem (APSP) is one of the foundational problems in computer science. For weighted dense graphs on $n$ vertices, no truly sub-cubic algorithms exist to compute APSP exactly even for undirected graphs. This is…
The GC problem is to identify a pre-determined number of center vertices such that the distances or costs from (or to) the centers to (or from) other vertices is minimized. The bottleneck of a path is the minimum capacity of edges on the…
Very recently a new algorithm to the nonnegative single-source shortest path problem on road networks has been discovered. It is very cache-efficient, but only on static road networks. We show how to augment it to the time-dependent…
In this paper we provide new randomized algorithms with improved runtimes for solving linear programs with two-sided constraints. In the special case of the minimum cost flow problem on $n$-vertex $m$-edge graphs with integer…
We provide universally-optimal distributed graph algorithms for $(1+\varepsilon)$-approximate shortest path problems including shortest-path-tree and transshipment. The universal optimality of our algorithms guarantees that, on any $n$-node…
In this paper, we consider the Constant-cost Orienteering Problem (COP) where a robot, constrained by a limited travel budget, aims at selecting a path with the largest reward in an aisle-graph. The aisle-graph consists of a set of loosely…
Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…
Computing the connected components of a graph is a fundamental problem in algorithmic graph theory. A major question in this area is whether we can compute connected components in $o(\log n)$ parallel time. Recent works showed an…
Let $G=(V,E,w)$ be a weighted directed graph without negative cycles. For two vertices $s,t\in V$, we let $d_{\le h}(s,t)$ be the minimum, according to the weight function $w$, of a path from $s$ to $t$ that uses at most $h$ edges, or hops.…
Graph-based nearest neighbor search methods have seen a surge of popularity in recent years, offering state-of-the-art performance across a wide variety of applications. Central to these methods is the task of constructing a sparse…
Using the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road…
In this paper, we study the Multi-Period Optimal Power Flow problem (MOPF) with electric vehicles (EV) under emission considerations. We integrate three different real-world datasets: household electricity consumption, marginal emission…
The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…
We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…
In this paper we present an $\tilde{O}(m\sqrt{n}\log^{O(1)}U)$ time algorithm for solving the maximum flow problem on directed graphs with $m$ edges, $n$ vertices, and capacity ratio $U$. This improves upon the previous fastest running time…
This paper presents a modeling and optimization framework to design battery electric micromobility vehicles, minimizing their total cost of ownership (TCO). Specifically, we first identify a model of the electric powertrain of an e-scooter…