arXiv subjects

Alice Paul

Publications and source records attributed to Alice Paul.

7 recordsLinked to original sources

arXiv2023

Estimating Censored Spatial-Temporal Demand with Applications to Shared Micromobility

In shared micromobility networks, such as bike-share and scooter-share networks, using trip data to accurately estimate demand in docked and dockless systems is critical to analyzing how the system is operating, such as identifying the number of dissatisfied users, operational costs, and equity in access, especially for city officials. However, the distribution of available bikes affects the distribution of observed trips. Users may walk from an unobserved cell location to an available bike masking the true location of user demand, and users may look for a bike and not find one, which is unobserved user demand. In collaboration with city planners from Providence, R.I., we present a flexible and interpretable framework to estimate spatial-temporal demand as a spatial non-homogeneous Poisson process that explicitly models how users choose a bike, bridging the gap between the docked and dockless methodology. Further, we present computational experiments highlighting that our method provides more accurate estimates of demand when there is incomplete availability compared to previous methods, and we comment on the results of our algorithm on data from Providence's dockless scooter-share network. Our estimation algorithm is publicly available through an efficient and user-friendly application designed for other city planners and organizations to help inform system planning.

stat.CO↗

arXiv2023

The All-Pairs Vitality-Maximization (VIMAX) Problem

Traditional network interdiction problems focus on removing vertices or edges from a network so as to disconnect or lengthen paths in the network; network diversion problems seek to remove vertices or edges to reroute flow through a designated critical vertex or edge. We introduce the all-pairs vitality maximization problem (VIMAX), in which vertex deletion attempts to maximize the amount of flow passing through a critical vertex, measured as the all-pairs vitality of the vertex. The assumption in this problem is that in a network for which the structure is known but the physical locations of vertices may not be known (e.g. a social network), locating a person or asset of interest might require the ability to detect a sufficient amount of flow (e.g., communications or financial transactions) passing through the corresponding vertex in the network. We formulate VIMAX as a mixed integer program, and show that it is NP-Hard. We compare the performance of the MIP and a simulated annealing heuristic on both real and simulated data sets and highlight the potential increase in vitality of key vertices that can be attained by subset removal. We also present graph theoretic results that can be used to narrow the set of vertices to consider for removal.

math.OC↗

arXiv2020

Clustering with Semidefinite Programming and Fixed Point Iteration

We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear optimization. We show the vertices of the Max k-Cut relaxation correspond to partitions of the data into at most k sets. We also show the vertices are attractive fixed points of iterated linear optimization. Each step of this iterative process solves a relaxation of the closest vertex problem and leads to a new clustering problem where the underlying clusters are more clearly defined. Our experiments show that using fixed point iteration for rounding the Max k-Cut SDP relaxation leads to significantly better results when compared to randomized rounding.

math.OC↗

arXiv2020

Iterated Linear Optimization

We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular, we consider elliptopes and derive an algebraic characterization of their fixed points. We show that the attractive fixed points of an elliptope are exactly its vertices. Finally, we discuss how fixed point iteration can be used for rounding the solution of a semidefinite programming relaxation.

math.OC↗

arXiv2020

Easy Capacitated Facility Location Problems, with Connections to Lot-Sizing

In this note, we consider the capacitated facility location problem when the transportation costs of the instance satisfy the Monge property. We show that a straightforward dynamic program finds the optimal solution when the demands are polynomially bounded. When demands are not polynomially bounded, we give a fully polynomial-time approximation scheme by adapting an algorithm and analysis of Van Hoesel and Wagelmans.

cs.DS↗

arXiv2018

A Framework for Vehicle Routing Approximation Schemes in Trees

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 serve a set of clients, subject to various constraints. For example, in Minimum Makespan Vehicle Routing, the number of vehicles is fixed, and the objective is to minimize the longest distance traveled by a single vehicle. Our main insight is that we can often greatly restrict the set of potential solutions without adding too much to the optimal solution cost. This simplification relies on partitioning the tree into clusters such that there exists a near-optimal solution in which every vehicle that visits a given cluster takes on one of a few forms. In particular, only a small number of vehicles serve clients in any given cluster. By using these coarser building blocks, a dynamic programming algorithm can find a near-optimal solution in polynomial time. We show that the framework is flexible enough to give PTASs for many problems, including Minimum Makespan Vehicle Routing, Distance-Constrained Vehicle Routing, Capacitated Vehicle Routing, and School Bus Routing, and can be extended to the multiple depot setting.

cs.DS↗

arXiv2010

A Census of Vertices by Generations in Regular Tessellations of the Plane

We consider regular tessellations of the plane as infinite graphs in which $q$ edges and $q$ faces meet at each vertex, and in which $p$ edges and $p$ vertices surround each face. For $1/p + 1/q = 1/2$, these are tilings of the Euclidean plane; for $1/p + 1/q < 1/2 $, they are tilings of the hyperbolic plane. We choose a vertex as the origin, and classify vertices into generations according to their distance (as measured by the number of edges in a shortest path) from the origin. For all $p\ge 3$ and $q \ge 3$ with $1/p + 1/q \le 1/2 $, we determine the rational generating function giving the number of vertices in each generation.

math.CO↗