On Profit-Maximizing Pricing for the Highway and Tollbooth Problems

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 edges of \bT such that the total revenue made by selling the paths to the customers that can afford them is maximized. An important special case of this problem, known as the \emph{highway problem}, is when \bT is restricted to be a line. For the tollbooth problem, we present a randomized $O(\log n)$-approximation, improving on the current best $O(\log m)$-approximation. We also study a special case of the tollbooth problem, when all the paths that customers are interested in purchasing go towards a fixed root of \bT. In this case, we present an algorithm that returns a $(1-\epsilon)$-approximation, for any $\epsilon > 0$, and runs in quasi-polynomial time. On the other hand, we rule out the existence of an FPTAS by showing that even for the line case, the problem is strongly NP-hard. Finally, we show that in the \emph{coupon model}, when we allow some items to be priced below zero to improve the overall profit, the problem becomes even APX-hard

On approximating the TSP with intersecting neighborhoods

In the TSP with neighborhoods problem we are given a set of $n$ regions (neighborhoods) in the plane, and seek to find a minimum length TSP tour that goes through all the regions. We give two approximation algorithms for the case when the regions are allowed to intersect: We give the first $O(1)$-factor approximation algorithm for intersecting convex fat objects of comparable diameters where we are allowed to hit each object only at a finite set of specified points. The proof follows from two packing lemmas that are of independent interest. For the problem in its most general form (but without the specified points restriction) we give a simple $O(\log n)$-approximation algorithm

Social media for openness and accountability in the public sector: cases in the Greek context

This paper explores the use of government social media for opennessand accountability. The extant literature has highlighted the benefits of social media use in this context to enhance citizen participation and engagement in decision-making and policy development, facilitate openness and transparency efforts, and reduce corruption. Yet, there are limited studies that discuss those properties of social media that can afford openness and accountability, and their implications for policy and practise. To address these gaps, a study is conducted in the Greek context using interviews with top managers, policy makers, and relevant stakeholders across five initiatives. We discuss distinct affordances for openness and accountability, and propose their inclusion as building blocks of the national ICT policy for openness and accountability. Finally, we provide the implications of the affordances lens for policy and practise, the limitations of the study and future research avenues

A quasi-PTAS for profit-maximizing pricing on line graphs

We consider the problem of pricing items so as to maximize the profit made from selling these items. An instance is given by a set E of n items and a set of m clients, where each client is specified by one subset of E (the bundle of items he/she wants to buy), and a budget (valuation), which is the maximum price he is willing to pay for that subset. We restrict our attention to the model where the subsets can be arranged such that they form intervals of a line graph. Assuming an unlimited supply of any item, this problem is known as the highway problem and so far only an O(logn)-approximation algorithm is known. We show that a PTAS is likely to exist by presenting a quasi-polynomial time approximation scheme. We also combine our ideas with a recently developed quasi-PTAS for the unsplittable flow problem on line graphs to extend this approximation scheme to the limited supply version of the pricing problem

Dynamic Offline Conflict-Free Coloring for Unit Disks

Abstract. A conflict-free coloring for a given set of disks is a coloring of the disks such that for any point p on the plane there is a disk among the disks covering p having a color different from that of the rest of the disks that covers p. In the dynamic offline setting, a sequence of disks is given, we have to color the disks one-by-one according to the order of the sequence and maintain the conflict-free property at any time for the disks that are colored. This paper focuses on unit disks, i.e., disks with radius one. We give an algorithm that colors a sequence of n unit disks in the dynamic offline setting using O(log n) colors. The algorithm is asymptotically optimal because Ω(log n) colors is necessary to color some set of n unit disks for any value of n [9].

Approximation algorithms for Euclidean group TSP

In the Euclidean group Traveling Salesman Problem (TSP), we are given a set of points P in the plane and a set of m connected regions, each containing at least one point of P. We want to find a tour of minimum length that visits at least one point in each region. This unifies the TSP with Neighborhoods and the Group Steiner Tree problem. We give a (9.1a+1)-approximation algorithm for the case when the regions are disjoint a-fat objects with possibly varying size. This considerably improves the best results known, in this case, for both the group Steiner tree problem and the TSP with Neighborhoods problem. We also give the first O(1)-approximation algorithm for the problem with intersecting regions

Berge multiplication for monotone boolean dualization

Given the prime CNF representation φ of a monotone Boolean function f: {0, 1} n ↦ → {0, 1}, the dualization problem calls for finding the corresponding prime DNF representation ψ of f. A very simple method (called Berge multiplication [3, Page 52–53]) works by multiplying out the clauses of φ from left to right in some order, simplifying whenever possible using the absorption law. We show that for any monotone CNF φ, Berge multiplication can be done in subexponential time, and for many interesting subclasses of monotone CNF’s such as CNF’s with bounded size, bounded degree, bounded intersection, bounded conformality, an

Output-Sensitive Algorithms for Enumerating Minimal Transversals for Some Geometric Hypergraphs

We give a general framework for the problem of finding all minimal hitting sets of a family of objects in R d by another. We apply this framework to the following problems: (i) hitting hyper-rectangles by points in R d; (ii) stabbing connected objects by axis-parallel hyperplanes in R d; and (iii) hitting half-planes by points. For both the covering and hitting set versions, we obtain incremental polynomial-time algorithms, provided that the dimension d is fixed