Dispersing Obnoxious Facilities on a Graph

On Obnoxious Markets

Certain markets evoke popular discomfort, distrust and even outrage. Trade in arms, drugs, toxic waste, child labor and body parts, for example, elicits these reactions to different degrees. This paper asks—what is it about some markets that brings about these responses? It is argued that three key parameters—extremity, agency and inequality—have a bearing on our intuitive reactions and serve t...

The Obnoxious Center Problem on a Tree

The obnoxious center problem in a graph G asks for a location on an edge of the graph such that the minimum weighted distance from this point to a vertex of the graph is as large as possible. We derive algorithms with linear running time for the cases when G is a path or a star, thus improving previous results of Tamir. For subdivided stars we present an algorithm of running time O(n log n). Fo...

The obnoxious enter problem on a tree

Dispersing points on intervals

We consider a problem of dispersing points on disjoint intervals on a line. Given n pairwise disjoint intervals sorted on a line, we want to find a point in each interval such that the minimum pairwise distance of these points is maximized. Based on a greedy strategy, we present a linear time algorithm for the problem. Further, we also solve in linear time the cycle version of the problem where...

Strategy-Proof Mechanism for Obnoxious Facility Location on a Line

In the problem of obnoxious facility location, an obnoxious facility is located in an area. To maximize the social welfare, e.g., the sum of distances from all the agents to the facility, we have to get the true locations of each agent. However, each agent may misreport his/her location to stay far away from the obnoxious facility. In this paper, we design strategy-proof mechanisms on locating ...