This work is a survey on a special minsum-maxmin bicriteria problem, known as the quickest path problem, that can model the transmission of data between two nodes of a network. Moreover, the authors review the problems of ranking the K quickest paths, and the K quickest loopless paths, and compare them in terms of the worst-case complexity order. The classification presented led to the proposal...

In a dynamic network, the quickest path problem asks for a path minimizing the time needed to send a given amount of flow from source to sink along this path. In practical settings, for example in evacuation or transportation planning, the reliability of network arcs depends on the specific scenario of interest. In this circumstance, the question of finding a quickest path among all those havin...

This thesis discusses optimization problems and equilibrium in networks. There are three major parts of the thesis. In the first part, we discuss optimization in dynamic networks. We focus on two fundamental optimization problems in dynamic networks: the quickest flow problem and the quickest transshipment problem. The quickest flow problem is to find a minimum time needed to send a given amoun...

Due to the increasing role of quickest paths for on-demand routing in computer networks, it is important to compute them faster, perhaps, by trading-o3 the quality for computational speed. We consider the computation of a quickest path from a source node to a destination node for a given message size in a network with n nodes and m links each of which is speci6ed by bandwidth and delay. Every k...

The paper deals with the quickest detection of a change of the drift of the Brownian motion. We show that the generalized Bayesian formulation of the quickest detection problem can be reduced to the optimal stopping problem for a diffusion Markov process. For this problem the optimal procedure is described and its characteristics are found. We show also that the same procedure is asymptotically...

Consider the following modification to the shortest path query problem in polygonal domains: instead of finding shortest path to a query point q, we find the shortest path to any point that sees q. We present an interactive visualization applet visualizing these quickest visibility paths. The applet also visualizes quickest visibility maps, that is the subdivision of the domain into cells by th...

We consider how local and global decision policies interact in stopping time problems such as quickest time change detection. Individual agents make myopic local decisions via social learning, that is, each agent records a private observation of a noisy underlying state process, selfishly optimizes its local utility and then broadcasts its local decision. Given these local decisions, how can a ...