arXiv subjects
Publications and source records attributed to Sándor P. Fekete.
In 1991, Edelsbrunner and Tan gave an O(n^2) algorithm for finding the MinMax Length triangulation of a set of points in the plane. In this paper we resolve one of the open problems stated in that paper, by showing that finding a MaxMin Length triangulation is an NP-complete problem. The proof implies that (unless P=NP), there is no polynomial-time approximation algorithm that can approximate the problem within any polynomial factor.
In this paper we consider methods for dynamically storing a set of different objects ("modules") in a physical array. Each module requires one free contiguous subinterval in order to be placed. Items are inserted or removed, resulting in a fragmented layout that makes it harder to insert further modules. It is possible to relocate modules, one at a time, to another free subinterval that is contiguous and does not overlap with the current location of the module. These constraints clearly distinguish our problem from classical memory allocation. We present a number of algorithmic results, including a bound of Theta(n^2) on physical sorting if there is a sufficiently large free space and sum up NP-hardness results for arbitrary initial layouts. For online scenarios in which modules arrive one at a time, we present a method that requires O(1) moves per insertion or deletion and amortized cost O(m_i log M) per insertion or deletion, where m_i is the module's size, M is the size of the largest module and costs for moves are linear in the size of a module.
In recent years, tremendous progress has been made in understanding the dynamics of vehicle traffic flow and traffic congestion by interpreting traffic as a multi-particle system. This helps to explain the onset and persistence of many undesired phenomena, e.g., traffic jams. It also reflects the apparent helplessness of drivers in traffic, who feel like passive particles that are pushed around by exterior forces; one of the crucial aspects is the inability to communicate and coordinate with other traffic participants. We present distributed methods for solving these fundamental problems, employing modern wireless, ad-hoc, multi-hop networks. The underlying idea is to use these capabilities as the basis for self-organizing methods for coordinating data collection and processing, recognizing traffic phenomena, and changing their structure by coordinated behavior. The overall objective is a multi-level approach that reaches from protocols for local wireless communication, data dissemination, pattern recognition, over hierarchical structuring and coordinated behavior, all the way to large-scale traffic regulation. In this article we describe three types of results: (i) self-organizing and distributed methods for maintaining and collecting data (using our concept of Hovering Data Clouds); (ii) adaptive data dissemination for traffic information systems; (iii) methods for self-recognition of traffic jams. We conclude by describing higher-level aspects of our work.