Amariah Becker
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View article: A PTAS for Minimum Makespan Vehicle Routing in Trees.
A PTAS for Minimum Makespan Vehicle Routing in Trees. Open
We develop a general framework for designing polynomial-time approximation schemes (PTASs) for various vehicle routing problems in trees. In these problems, the goal is to optimally route a fleet of vehicles, originating at a depot, to ser…
View article: Polynomial-Time Approximation Schemes for k-center, k-median, and Capacitated Vehicle Routing in Bounded Highway Dimension
Polynomial-Time Approximation Schemes for k-center, k-median, and Capacitated Vehicle Routing in Bounded Highway Dimension Open
The concept of bounded highway dimension was developed to capture observed properties of road networks. We show that a graph of bounded highway dimension with a distinguished root vertex can be embedded into a graph of bounded treewidth in…
View article: A Tight 4/3 Approximation for Capacitated Vehicle Routing in Trees
A Tight 4/3 Approximation for Capacitated Vehicle Routing in Trees Open
Given a set of clients with demands, the Capacitated Vehicle Routing problem is to find a set of tours that collectively cover all client demand, such that the capacity of each vehicle is not exceeded and such that the sum of the tour leng…
View article: Polynomial-Time Approximation Schemes for k-Center and Bounded-Capacity Vehicle Routing in Metrics with Bounded Highway Dimension.
Polynomial-Time Approximation Schemes for k-Center and Bounded-Capacity Vehicle Routing in Metrics with Bounded Highway Dimension. Open
The concept of bounded highway dimension was developed to capture observed properties of the metrics of road networks. We show that a graph with bounded highway dimension, for any vertex, can be embedded into a a graph of bounded treewidth…
View article: Polynomial-Time Approximation Schemes for k-Center and Bounded-Capacity Vehicle Routing in Graphs with Bounded Highway Dimension
Polynomial-Time Approximation Schemes for k-Center and Bounded-Capacity Vehicle Routing in Graphs with Bounded Highway Dimension Open
The concept of bounded highway dimension was developed to capture observed properties of the metrics of road networks. We show that a graph with bounded highway dimension, for any vertex, can be embedded into a a graph of bounded treewidth…
View article: Polynomial-Time Approximation Schemes for Bounded-Capacity Vehicle Routing and Clustering Problems in Metrics with Bounded Highway Dimension
Polynomial-Time Approximation Schemes for Bounded-Capacity Vehicle Routing and Clustering Problems in Metrics with Bounded Highway Dimension Open
The concept of bounded highway dimension was developed to capture observed properties of the metrics of road networks. We show that a metric with bounded highway dimension and a distinguished point (the depot) can be embedded into a a grap…
View article: A Quasi-Polynomial-Time Approximation Scheme for Vehicle Routing on Planar and Bounded-Genus Graphs
A Quasi-Polynomial-Time Approximation Scheme for Vehicle Routing on Planar and Bounded-Genus Graphs Open
The Capacitated Vehicle Routing problem is a generalization of the Traveling Salesman problem in which a set of clients must be visited by a collection of capacitated tours. Each tour can visit at most Q clients and must start and end at a…
View article: Engineering an Approximation Scheme for Traveling Salesman in Planar Graphs
Engineering an Approximation Scheme for Traveling Salesman in Planar Graphs Open
We present an implementation of a linear-time approximation scheme for the traveling salesman problem on planar graphs with edge weights. We observe that the theoretical algorithm involves constants that are too large for practical use. Ou…
View article: Capacitated Dominating Set on Planar Graphs
Capacitated Dominating Set on Planar Graphs Open
Capacitated Domination generalizes the classic Dominating Set problem by specifying for each vertex a required demand and an available capacity for covering demand in its closed neighborhood. The objective is to find a minimum-sized set of…
View article: Assessing the Department of Defense's Approach to Reducing Mental Health Stigma
Assessing the Department of Defense's Approach to Reducing Mental Health Stigma Open
When facing mental health problems, many service members choose not to seek needed help because of the stigma associated with mental health disorders and treatment. Not seeking appropriate mental healthcare can negatively impact the qualit…