Related papers: Minmax-Regret $k$-Sink Location on a Dynamic Tree …
In dynamic flow networks, every vertex starts with items (flow) that need to be shipped to designated sinks. All edges have two associated quantities: length, the amount of time required for a particle to traverse the edge, and capacity,…
Let $G=(V,E)$ be a graph modelling a building or road network in which edges have-both travel times (lengths) and capacities associated with them. An edge's capacity is the number of people that can enter that edge in a unit of time. In…
This paper addresses the minmax regret 1-sink location problem on dynamic flow path networks with parametric weights. We are given a dynamic flow network consisting of an undirected path with positive edge lengths, positive edge capacities,…
A dynamic path network is an undirected path with evacuees situated at each vertex. To evacuate the path, evacuees travel towards a designated sink (doorway) to exit. Each edge has a capacity, the number of evacuees that can enter the edge…
This paper considers the k-sink location problem in dynamic path networks. In our model, a dynamic path network consists of an undirected path with positive edge lengths, uniform edge capacity, and positive vertex supplies. Here, each…
Evacuation in emergency situations can be modeled by a dynamic flow network. Two criteria have been used before: one is the evacuation completion time and the other is the aggregate evacuation time of individual evacuees. The aim of this…
Let $T=(V,E)$ be a tree with associated costs on its subtrees. A minmax $k$-partition of $T$ is a partition into $k$ subtrees, minimizing the maximum cost of a subtree over all possible partitions. In the centered version of the problem,…
A dynamic flow network consists of a directed graph, where nodes called sources represent locations of evacuees, and nodes called sinks represent locations of evacuation facilities. Each source and each sink are given supply representing…
A Dynamic Graph Network is a graph in which each edge has an associated travel time and a capacity (width) that limits the number of items that can travel in parallel along that edge. Each vertex in this dynamic graph network begins with…
This paper considers the minimax regret 1-median problem in dynamic path networks. In our model, we are given a dynamic path network consisting of an undirected path with positive edge lengths, uniform positive edge capacity, and…
We consider the problem of locating a set of $k$ sinks on a path network with general edge capacities that minimizes the sum of the evacuation times of all evacuees. We first present an $O(kn\log^4n)$ time algorithm when the edge capacities…
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…
A dynamic network ${\cal N} = (G,c,\tau,S)$ where $G=(V,E)$ is a graph, integers $\tau(e)$ and $c(e)$ represent, for each edge $e\in E$, the time required to traverse edge $e$ and its nonnegative capacity, and the set $S\subseteq V$ is a…
This paper addresses a version of the single-facility Maximal Covering Location Problem on a network where the demand is: (i) distributed along the edges and (ii) uncertain with only a known interval estimation. To deal with this problem,…
In this paper, we propose new algorithms for evacuation problems defined on dynamic flow networks. A dynamic flow network is a directed graph in which source nodes are given supplies (i.e., the number of evacuees) and a single sink node is…
We study dynamic clustering problems from the perspective of online learning. We consider an online learning problem, called \textit{Dynamic $k$-Clustering}, in which $k$ centers are maintained in a metric space over time (centers may…
In this paper the minmax (regret) versions of some basic polynomially solvable deterministic network problems are discussed. It is shown that if the number of scenarios is unbounded, then the problems under consideration are not…
In this research, we examine the minsum flow problem in dynamic path networks where flows are represented as discrete and weighted sets. The minsum flow problem has been widely studied for its relevance in finding evacuation routes during…
Dynamic Flows were introduced by Ford and Fulkerson in 1958 to model flows over time. They define edge capacities to be the total amount of flow that can enter an edge {\em in one time unit}. Each edge also has a length, representing the…
Regret minimizing sets are a very recent approach to representing a dataset D with a small subset S of representative tuples. The set S is chosen such that executing any top-1 query on S rather than D is minimally perceptible to any user.…