Related papers: A Sublogarithmic Approximation for Highway and Tol…
In the \emph{tollbooth problem}, we are given a tree $\bT=(V,E)$ with $n$ edges, and a set of $m$ customers, each of whom is interested in purchasing a path on the tree. Each customer has a fixed budget, and the objective is to price the…
We study an envy-free pricing problem, in which each buyer wishes to buy a shortest path connecting her individual pair of vertices in a network owned by a single vendor. The vendor sets the prices of individual edges with the aim of…
In the highway problem, we are given an n-edge line graph (the highway), and a set of paths (the drivers), each one with its own budget. For a given assignment of edge weights (the tolls), the highway owner collects from each driver the…
We study the worst-case welfare of item pricing in the \emph{tollbooth problem}. The problem was first introduced by Guruswami et al, and is a special case of the combinatorial auction in which (i) each of the $m$ items in the auction is an…
We consider the single-source (or single-sink) buy-at-bulk problem with an unknown concave cost function. We want to route a set of demands along a graph to or from a designated root node, and the cost of routing x units of flow along an…
Consider a graph $G = (V, E)$ and some commuters, each specified by a tuple $(u, v, b)$ consisting of two nodes in the graph $u, v \in V$ and a non-negative real number $b$, specifying their budget. The goal is to find a pricing function…
We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly…
We study the network pricing problem where the leader maximizes their revenue by determining the optimal amounts of tolls to charge on a set of arcs, under the assumption that the followers will react rationally and choose the shortest…
This paper studies a fundamental algorithmic problem related to the design of demand-aware networks: networks whose topologies adjust toward the traffic patterns they serve, in an online manner. The goal is to strike a tradeoff between the…
When a store sells items to customers, the store wishes to determine the prices of the items to maximize its profit. Intuitively, if the store sells the items with low (resp. high) prices, the customers buy more (resp. less) items, which…
We give polynomial time logarithmic approximation guarantees for the budget minimization, as well as for the profit maximization versions of minimum spanning tree interdiction. In this problem, the goal is to remove some edges of an…
Tolls are collected on many highways as a means of traffic control and revenue generation. However, the presence of tollbooths on highway surely slows down traffic flow. Here, we investigate how the presence of tollbooths affect the average…
In the Stackelberg Network Pricing problem, one has to assign tariffs to a certain subset of the arcs of a given transportation network. The aim is to maximize the amount paid by the user of the network, knowing that the user will take a…
The profitable tour problem (PTP) is a well-known NP-hard routing problem searching for a tour visiting a subset of customers while maximizing profit as the difference between total revenue collected and traveling costs. PTP is known to be…
We consider the indirect covering subtree problem (Kim et al., 1996). The input is an edge weighted tree graph along with customers located at the nodes. Each customer is associated with a radius and a penalty. The goal is to locate a…
We consider the Stackelberg shortest-path pricing problem, which is defined as follows. Given a graph G with fixed-cost and pricable edges and two distinct vertices s and t, we may assign prices to the pricable edges. Based on the…
Consider a transportation problem with sets of sources and sinks. There are profits and prices on the edges. The goal is to maximize the profit while meeting the following constraints; the total flow going out of a source must not exceed…
We study the single-sink buy-at-bulk problem with an unknown cost function. We wish to route flow from a set of demand nodes to a root node, where the cost of routing x total flow along an edge is proportional to f(x) for some concave,…
We study a robust toll pricing problem where toll setters and users have different level of information when taking their decisions. Toll setters do not have full information on the costs of the network and rely on historical information…
This paper considers the vehicle routing problem with stochastic demands (VRPSD) under optimal restocking. We develop an exact algorithm that is effective for solving instances with many vehicles and few customers per route. In our…