Related papers: Sublogarithmic Approximation for Tollbooth Pricing…
Given a graph with edge costs and vertex profits and given a budget B, the Orienteering Problem asks for a walk of cost at most B of maximum profit. Additionally, each profit may be given with a time window within it can be collected by the…
Consider the following toy problem. There are $m$ rectangles and $n$ points on the plane. Each rectangle $R$ is a consumer with budget $B_R$, who is interested in purchasing the cheapest item (point) inside R, given that she has enough…
We study a market mechanism that sets edge prices to incentivize strategic agents to efficiently share limited network capacity. In this market, agents form coalitions, with each coalition sharing a unit capacity of a selected route and…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
The symmetric Virtual Private Network Design (VPND) problem is concerned with buying capacity on links (edges) in a communication network such that certain traffic demands can be met. We investigate a natural generalization of VPND where…
We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent…
We consider some classical optimization problems in path planning and network transport, and we introduce new auction-based algorithms for their optimal and suboptimal solution. The algorithms are based on mathematical ideas that are…
We consider markets consisting of a set of indivisible items, and buyers that have {\em sharp} multi-unit demand. This means that each buyer $i$ wants a specific number $d_i$ of items; a bundle of size less than $d_i$ has no value, while a…
We study the knapsack problem with graph theoretic constraints. That is, we assume that there exists a graph structure on the set of items of knapsack and the solution also needs to satisfy certain graph theoretic properties on top of…
We consider the problem of choosing prices of a set of products so as to maximize profit, taking into account self-elasticity and cross-elasticity, subject to constraints on the prices. We show that this problem can be formulated as…
In the last decade, charging service providers are emerging along with the prevalence of electric vehicles. These providers need to strategically optimize their charging prices to improve the profits considering operation conditions of the…
The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network. Its edges are colored either red or blue, and the red edges have a given fixed cost, representing the…
We study a sequential profit-maximization problem, optimizing for both price and ancillary variables like marketing expenditures. Specifically, we aim to maximize profit over an arbitrary sequence of multiple demand curves, each dependent…
We study an online revenue maximization problem where the consumers arrive i.i.d from some unknown distribution and purchase a bundle of products from the sellers. The classical approach generally assumes complete knowledge of the consumer…
The online (uniform) buy-at-bulk network design problem asks us to design a network, where the edge-costs exhibit economy-of-scale. Previous approaches to this problem used tree- embeddings, giving us randomized algorithms. Moreover, the…
Temporal dependencies between customer visits, such as synchronization constraints, pose a fundamental challenge in vehicle routing. These dependencies, which arise in applications such as home healthcare routing, aircraft scheduling, and…
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…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
A network for the transportation of supplies can be described as a rooted tree with a weight of a degree of congestion for each edge. We take the sum of root-leaf distance (SRD) on a rooted tree as the whole degree of congestion of the…
In this paper we study a revenue maximization problem for optical routing nodes. We model the routing node as a single server polling model with the aim to assign visit periods (service windows) to the different stations (ports) such that…