Related papers: Optimal Longest Paths by Dynamic Programming
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…
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.…
Computing shortest paths is one of the most fundamental algorithmic graph problems. It is known since decades that this problem can be solved in near-linear time if all weights are nonnegative. A recent break-through by [Bernstein,…
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…
Finding optimal paths in connected graphs requires determining the smallest total cost for traveling along the graph's edges. This problem can be solved by several classical algorithms where, usually, costs are predefined for all edges.…
The problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertex-colored temporal graph, asks for a path whose vertices have…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic…
The $k$ disjoint shortest paths problem ($k$-DSPP) on a graph with $k$ source-sink pairs $(s_i, t_i)$ asks for the existence of $k$ pairwise edge- or vertex-disjoint shortest $s_i$-$t_i$-paths. It is known to be NP-complete if $k$ is part…
We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an…
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…
A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…
Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of…
Although Dijkstra's algorithm has near-optimal time complexity for the problem of finding a shortest path from a given vertex $s$ to a given vertex $t$, in practice other algorithms are often superior on huge graphs. A prominent example is…
Computing paths in graph structures is a fundamental operation in a wide range of applications, from transportation networks to data analysis. The beer path problem, which captures the option of visiting points of interest, such as gas…
Many real-world systems, such as social networks, rely on mining efficiently large graphs, with hundreds of millions of vertices and edges. This volume of information requires partitioning the graph across multiple nodes in a distributed…
This paper presents a triple optimization algorithm of two-dimensional space, driving path and driving speed, and iterates in the time dimension to obtain the local optimal solution of path and speed in the optimal driving area. Design…
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…
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…