Related papers: Shortest paths with a cost constraint: a probabili…
In a temporal graph, each edge is available at specific points in time. Such an availability point is often represented by a ''temporal edge'' that can be traversed from its tail only at a specific departure time, for arriving in its head…
Resource constrained shortest path problems are usually solved thanks to a smart enumeration of all the non-dominated paths. Recent improvements of these enumeration algorithms rely on the use of bounds on path resources to discard partial…
The search is based on the preliminary transformation of matrices or adjacency lists traditionally used in the study of graphs into projections cleared of redundant information (refined) followed by the selection of the desired shortest…
We present an algorithm for the k shortest simple path problem on weighted directed graphs (kSSP) that is based on Eppstein's algorithm for a similar problem in which paths are allowed to contain cycles. In contrast to most other algorithms…
The computation of short paths in graphs with arc lengths is a pillar of graph algorithmics and network science. In a more diverse world, however, not every short path is equally valuable. For the setting where each vertex is assigned to a…
For a graph $G$ and $p\in [0,1]$, let $G_p$ arise from $G$ by deleting every edge mutually independently with probability $1-p$. The random graph model $(K_n)_p$ is certainly the most investigated random graph model and also known as the…
We consider the length of {\em ordered loose paths} in the random $r$-uniform hypergraph $H=H^{(r)}(n, p)$. A ordered loose path is a sequence of edges $E_1,E_2,\ldots,E_\ell$ where $\max\{j\in E_i\}=\min\{j\in E_{i+1}\}$ for $1\leq…
Various applications of graphs, in particular applications related to finding shortest paths, naturally get inputs with real weights on the edges. However, for algorithmic or visualization reasons, inputs with integer weights would often be…
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for…
While the shortest path problem has myriad applications, the computational efficiency of suitable algorithms depends intimately on the underlying problem domain. In this paper, we focus on domains where evaluating the edge weight function…
In this work we study the time complexity for the search of local minima in random graphs whose vertices have i.i.d. cost values. We show that, for Erd\"os-R\'enyi graphs with connection probability given by $\lambda/n^\alpha$ (with…
We consider the problem of minimizing the number of triangles in a graph of given order and size and describe the asymptotic structure of extremal graphs. This is achieved by characterizing the set of flag algebra homomorphisms that…
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…
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…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…
The edges of a graph are assigned weights and passage times which are assumed to be positive integers. We present a parallel algorithm for finding the shortest path whose total weight is smaller than a pre-determined value. In each step the…
We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. We obtain $poly(\log\log n)$-round algorithms for the following problems in unweighted undirected…
This work is devoted to lower bounds on independence numbers of distance graphs with vertices in $\{-1,0,1\}^n$. The asymptotic case is studied, yielding new results over a broad range of parameters. Numerical results are presented,…
Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path planning on graphs. Our approach is based on augmenting the state…