We study the problem of embedding shortest-path metrics weighted graphs into $\ell_p$ spaces. introduce a new technique based on low-depth decompositions graph via shortest paths. The notion Shortest Path Decomposition depth is inductively defined: A (weighed) path has decomposition (SPD) $1$. General an SPD $k$ if it contains whose deletion leads to graph, each components at most $k-1$. In thi...

Real-time vehicle guidance effectively reduces traffic jams and improves the operational efficiency of urban transportation. The trip time on a route is considered as random process that changes with time, shortest path selection requires dynamic model solution decision-making problem. Thus, criterion to determine by programming (DP) which discretizes times in continuous segments route. In this...

We consider Euclidean first-passage percolation on a large family of connected random geometric graphs in the d-dimensional Euclidean space encompassing various well-known models from stochastic geometry. In particular, we establish a strong linear growth property for shortest-path lengths on random geometric graphs which are generated by point processes. We consider the event that the growth o...

In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. We also present a linear time logspace shortest path algorithm for graphs with bounded vertex degree and biconnected component size, which does not rely on an oracle. ...

Abstract. We extend the Stochastic Subscriber Line Model by the introduction of shortest-path trees which are obtained by splitting up the segment system of the typical serving zone at its crossings and endings. Due to reasons in the complex field of cost and capacity estimation in telecommunication networks, it is desirable to gain knowledge about distributional properties of the branches of t...

How to model traveler’s perception of travel time is always an important issue in the development of traffic assignment models. Since travelers rarely have perfect knowledge of the road network or of the traveling conditions, they choose routes based on their perceived travel times. Traditionally, travelers’ perceived travel times are treated as random variables, leading to the stochastic traff...

We consider the stochastic shortest path problem, a classical finite-state Markovian decision problem with a termination state, and we propose new convergent Q-learning algorithms that combine elements of policy iteration and classical Q-learning/value iteration. These algorithms are related to the ones introduced by the authors for discounted problems in Bertsekas and Yu (Math. Oper. Res. 37(1...

We consider first-passage percolation on segment processes and provide concentration results concerning moderate deviations of shortest-path lengths from a linear function in the distance of their endpoints. The proofs are based on a martingale technique developed by H. Kesten for an analogous problem on the lattice. Our results are applicable to graph models from stochastic geometry. For examp...