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We combine the well known Shortest Paths (SP) problem and the Bottleneck Paths (BP) problem to introduce a new problem called the Shortest Paths for All Flows (SP-AF) problem that has relevance in real life applications. We first solve the…
The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a…
We study the problem of computing shortest paths in so-called dense distance graphs. Every planar graph $G$ on $n$ vertices can be partitioned into a set of $O(n/r)$ edge-disjoint regions (called an $r$-division) with $O(r)$ vertices each,…
Given in the plane a set $S$ of $n$ points and a set of disks centered at these points, the disk graph $G(S)$ induced by these disks has vertex set $S$ and an edge between two vertices if their disks intersect. Note that the disks may have…
This paper studies a combinatorial optimization problem which is obtained by combining the flow shop scheduling problem and the shortest path problem. The objective of the obtained problem is to select a subset of jobs that constitutes a…
The single-source shortest path problem is a classical problem in the research field of graph algorithm. In this paper, a new single-source shortest path algorithm for nonnegative weight graph is proposed. The algorithm can compress…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
This paper presents a new anytime algorithm for the marginal MAP problem in graphical models. The algorithm is described in detail, its complexity and convergence rate are studied, and relations to previous theoretical results for the…
In this paper we provide an algorithm which given any $m$-edge $n$-vertex directed graph with integer capacities at most $U$ computes a maximum $s$-$t$ flow for any vertices $s$ and $t$ in $m^{11/8+o(1)}U^{1/4}$ time with high probability.…
One of the most popular approaches to multi-target tracking is tracking-by-detection. Current min-cost flow algorithms which solve the data association problem optimally have three main drawbacks: they are computationally expensive, they…
Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is…
Platooning connected and autonomous vehicles (CAVs) provide significant benefits in terms of traffic efficiency and fuel economy. However, most existing platooning systems assume the availability of pre-determined plans, which is not…
Shortest path queries over graphs are usually considered as isolated tasks, where the goal is to return the shortest path for each individual query. In practice, however, such queries are typically part of a system (e.g., a road network)…
We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…
In this paper we study a property of time-dependent graphs, dubbed path ranking invariance. Broadly speaking, a time-dependent graph is path ranking invariant if the ordering of its paths (w.r.t. travel time) is independent of the start…
We address the facility location problems on dynamic flow path networks. A dynamic flow path network consists of an undirected path with positive edge lengths, positive edge capacities, and positive vertex weights. A path can be considered…
We present theoretical and numerical results concerning the problem to find the path that minimizes the time to navigate between two given points in a complex fluid under realistic navigation constraints. We contrast deterministic Optimal…
We consider the problem of computing shortest paths in a dense motion-planning roadmap $\mathcal{G}$. We assume that~$n$, the number of vertices of $\mathcal{G}$, is very large. Thus, using any path-planning algorithm that directly searches…
Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…