Sándor P. Fekete

Deterministic boundary recognition and topology extraction for large sensor networks

We present a new framework for the crucial challenge of self-organization of a large sensor network. The basic scenario can be described as follows: Given a large swarm of immobile sensor nodes that have been scattered in a polygonal region, such as a street network. Nodes have no knowledge of size or shape of the environment or the position of other nodes. Moreover, they have no way of measuring coordinates, geometric distances to other nodes, or their direction. Their only way of interacting with other nodes is to send or to receive messages from any node that is within communication range. The objective is to develop algorithms and protocols that allow self-organization of the swarm into large-scale structures that reflect the structure of the street network, setting the stage for global routing, tracking and guiding algorithms.Our algorithms work in two stages: boundary recognition and topology extraction. All steps are strictly deterministic, yield fast distributed algorithms, and make no assumption on the distribution of nodes in the environment, other than sufficient density.

Neighborhood-Based Topology Recognition in Sensor Networks

We consider a crucial aspect of self-organization of a sensor network consisting of a large set of simple sensor nodes with no location hardware and only very limited communication range. After having been distributed randomly in a given two-dimensional region, the nodes are required to develop a sense for the environment, based on a limited amount of local communication. We describe algorithmic approaches for determining the structure of boundary nodes of the region, and the topology of the region. We also develop methods for determining the outside boundary, the distance to the closest boundary for each point, the Voronoi diagram of the different boundaries, and the geometric thickness of the network. Our methods rely on a number of natural assumptions that are present in densely distributed sets of nodes, and make use of a combination of stochastics, topology, and geometry. Evaluation requires only a limited number of simple local computations.

An Exact Algorithm for Higher-Dimensional Orthogonal Packing

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of lower bounds, and other heuristics, we develop a two-level tree search algorithm for solving higher-dimensional packing problems to optimality. Computational results are reported, including optimal solutions for all two-dimensional test problems from recent literature. This is the third in a series of articles describing new approaches to higher-dimensional packing.

New classes of fast lower bounds for bin packing problems

Abstract.The bin packing problem is one of the classical NP-hard optimization problems. In this paper, we present a simple generic approach for obtaining new fast lower bounds, based on dual feasible functions. Worst-case analysis as well as computational results show that one of our classes clearly outperforms the previous best “economical” lower bound for the bin packing problem by Martello and Toth, which can be understood as a special case. In particular, we prove an asymptotic worst-case performance of 3/4 for a bound that can be computed in linear time for items sorted by size. In addition, our approach provides a general framework for establishing new bounds.

Approximation algorithms for lawn mowing and milling

Abstract We study the problem of finding shortest tours/paths for “lawn mowing” and “milling” problems: Given a region in the plane, and given the shape of a “cutter” (typically, a circle or a square), find a shortest tour/path for the cutter such that every point within the region is covered by the cutter at some position along the tour/path. In the milling version of the problem, the cutter is constrained to stay within the region. The milling problem arises naturally in the area of automatic tool path generation for NC pocket machining. The lawn mowing problem arises in optical inspection, spray painting, and optimal search planning. Both problems are NP-hard in general. We give efficient constant-factor approximation algorithms for both problems. In particular, we give a (3+e) -approximation algorithm for the lawn mowing problem and a 2.5-approximation algorithm for the milling problem. Furthermore, we give a simple 6 5 -approximation algorithm for the TSP problem in simple grid graphs, which leads to an 11 5 -approximation algorithm for milling simple rectilinear polygons.

DyNoC: A dynamic infrastructure for communication in dynamically reconfugurable devices

A new paradigm to support the communication among modules dynamically placed on a reconfigurable device at run-time is presented. Based on the network on chip (NoC) infrastructure, we developed a dynamic communication infrastructure as well as routing methodologies capable to handle routing in a NoC with obstacles created by dynamically placed components. We prove the unrestricted reachability of components and pins, the deadlock-freeness and we finally show the feasibility of our approach by means on real life example applications.

A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for instance in two- or higher-dimensional space. We present a new approach for modeling packings, using a graph-theoretical characterization of feasible packings. Our characterization allows it to deal with classes of packings that share a certain combinatorial structure, instead of having to consider one packing at a time. In addition, we can make use of elegant algorithmic properties of certain classes of graphs. This allows our characterization to be the basis for a successful branch-and-bound framework.This is the first in a series of papers describing new approaches to higher-dimensional packing.

Two Dimensional Rendezvous Search

We consider rendezvous problems in which two players move on the plane and wish to cooperate to minimise their first meeting time. We begin by considering the case where both players are placed such that the vector difference is chosen equiprobably from a finite set. We also consider a situation in which they know they are a distanced apart, but they do not know the direction of the other player. Finally, we give some results for the case in which player 1 knows the initial position of player 2, while player 2 is given information only on the initial distance of player 1.

SpyGlass: a wireless sensor network visualizer

In this paper we present a modular and extensible visualization framework for wireless sensor networks. These networks have typically no means of visualizing their internal state, sensor readings or computational results. Visualization is therefore a key issue to develop and operate these networks. Data emitted by individual sensor nodes is collected by gateway software running on a machine in the sensor network. It is then passed on via TCP/IP to the visualization software on a potentially remote machine. Visualization plug-ins can register to different data types, and visualize the information using a flexible multi-layer mechanism that renders the information on a canvas. Developers can easily adapt existing or develop new custom tailored plug-ins for their specific visualization needs and applications.

Optimal Covering Tours with Turn Costs

We give the first algorithmic study of a class of “covering tour” problems related to the geometric Traveling Salesman Problem: Find a polygonal tour for a cutter so that it sweeps out a specified region (“pocket”), in order to minimize a cost that depends not only on the length of the tour but also on the number of turns. These problems arise naturally in manufacturing applications of computational geometry to automatic tool path generation and automatic inspection systems, as well as arc routing (“postman”) problems with turn penalties. We prove lower bounds (NP-completeness of minimum-turn milling) and give efficient approximation algorithms for several natural versions of the problem, including a polynomial-time approximation scheme based on a novel adaptation of the m-guillotine method.