arXiv subjects

Sandor P. Fekete

Publications and source records attributed to Sandor P. Fekete.

At least 37 records · Page 2Linked to original sources

arXiv2008

Staged Self-Assembly:Nanomanufacture of Arbitrary Shapes with O(1) Glues

We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are motivated by a practical nanofabrication scenario through protein-based bioengineering. Staging allows us to break through the traditional lower bounds in tile self-assembly by encoding the shape in the staging algorithm instead of the tiles. All of our results are based on the practical assumption that only a constant number of glues, and thus only a constant number of tiles, can be engineered, as each new glue type requires significant biochemical research and experiments. Under this assumption, traditional tile self-assembly cannot even manufacture an n*n square; in contrast, we show how staged assembly enables manufacture of arbitrary orthogonal shapes in a variety of precise formulations of the model.

cs.CG↗

arXiv2006

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; see cs.DS/0310032 and cs.DS/0402044.

cs.DS↗

arXiv2006

Minimum-Cost Coverage of Point Sets by Disks

We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (t_j) and radii (r_j) that cover a given set of demand points Y in the plane at the smallest possible cost. We consider cost functions of the form sum_j f(r_j), where f(r)=r^alpha is the cost of transmission to radius r. Special cases arise for alpha=1 (sum of radii) and alpha=2 (total area); power consumption models in wireless network design often use an exponent alpha>2. Different scenarios arise according to possible restrictions on the transmission centers t_j, which may be constrained to belong to a given discrete set or to lie on a line, etc. We obtain several new results, including (a) exact and approximation algorithms for selecting transmission points t_j on a given line in order to cover demand points Y in the plane; (b) approximation algorithms (and an algebraic intractability result) for selecting an optimal line on which to place transmission points to cover Y; (c) a proof of NP-hardness for a discrete set of transmission points in the plane and any fixed alpha>1; and (d) a polynomial-time approximation scheme for the problem of computing a minimum cost covering tour (MCCT), in which the total cost is a linear combination of the transmission cost for the set of disks and the length of a tour/path that connects the centers of the disks.

cs.DS↗

arXiv2005

Communication-Aware Processor Allocation for Supercomputers

This paper gives processor-allocation algorithms for minimizing the average number of communication hops between the assigned processors for grid architectures, in the presence of occupied cells. The simpler problem of assigning processors on a free grid has been studied by Karp, McKellar, and Wong who show that the solutions have nontrivial structure; they left open the complexity of the problem. The associated clustering problem is as follows: Given n points in Re^d, find k points that minimize their average pairwise L1 distance. We present a natural approximation algorithm and show that it is a 7/4-approximation for 2D grids. For d-dimensional space, the approximation guarantee is 2-(1/2d), which is tight. We also give a polynomial-time approximation scheme (PTAS) for constant dimension d, and report on experimental results.

cs.DS↗

arXiv2005

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.

cs.DC↗

arXiv2005

DyNoC: A Dynamic Infrastructure for Communication in Dynamically Reconfigurable 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.

cs.AR↗

arXiv2005

The Freeze-Tag Problem: How to Wake Up a Swarm of Robots

An optimization problem that naturally arises in the study of swarm robotics is the Freeze-Tag Problem (FTP) of how to awaken a set of ``asleep'' robots, by having an awakened robot move to their locations. Once a robot is awake, it can assist in awakening other slumbering robots.The objective is to have all robots awake as early as possible. While the FTP bears some resemblance to problems from areas in combinatorial optimization such as routing, broadcasting, scheduling, and covering, its algorithmic characteristics are surprisingly different. We consider both scenarios on graphs and in geometric environments.In graphs, robots sleep at vertices and there is a length function on the edges. Awake robots travel along edges, with time depending on edge length. For most scenarios, we consider the offline version of the problem, in which each awake robot knows the position of all other robots. We prove that the problem is NP-hard, even for the special case of star graphs. We also establish hardness of approximation, showing that it is NP-hard to obtain an approximation factor better than 5/3, even for graphs of bounded degree.These lower bounds are complemented with several positive algorithmic results, including: (1) We show that the natural greedy strategy on star graphs has a tight worst-case performance of 7/3 and give a polynomial-time approximation scheme (PTAS) for star graphs. (2) We give a simple O(log D)-competitive online algorithm for graphs with maximum degree D and locally bounded edge weights. (3) We give a PTAS, running in nearly linear time, for geometrically embedded instances.

cs.DS↗

arXiv2005

PackLib^2: An integrated library of multi-dimensional packing problems

We present PackLib^2, the first fully integrated benchmark library for multi-dimensional packing instances. PackLib^2 combines a systematic collection of all benchmark instances from previous literature with a well-organized set of new and challenging large instances. The XML format allows linking basic benchmark data with other important properties, like bibliographic information, origin, best known solutions, runtimes, etc. Transforming instances into a variety of existing input formats is also quite easy, as the XML format lends itself to easy conversion; for this purpose, a number of parsers are provided. Thus, PackLib^2 aims at becoming a one-stop location for the packing and cutting community: In addition to fair and easy comparison of algorithmic work and ongoing measurement of scientific progress, it poses numerous challenges for future research.

math.OC↗

arXiv2005

A New Approach for Boundary Recognition in Geometric Sensor Networks

We describe a new approach for dealing with the following central problem in the self-organization of a geometric sensor network: Given a polygonal region R, and a large, dense set of sensor nodes that are scattered uniformly at random in R. There is no central control unit, and nodes can only communicate locally by wireless radio to all other nodes that are within communication radius r, without knowing their coordinates or distances to other nodes. The objective is to develop a simple distributed protocol that allows nodes to identify themselves as being located near the boundary of R and form connected pieces of the boundary. We give a comparison of several centrality measures commonly used in the analysis of social networks and show that restricted stress centrality is particularly suited for geometric networks; we provide mathematical as well as experimental evidence for the quality of this measure.

cs.DS↗

arXiv2005

Higher-Dimensional Packing with Order Constraints

We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional generalizations of scheduling problems. Using graph-theoretic structures to describe feasible solutions, we develop a novel exact branch-and-bound algorithm. This extends previous work by Fekete and Schepers; a key tool is a new order-theoretic characterization of feasible extensions of a partial order to a given complementarity graph that is tailor-made for use in a branch-and-bound environment. The usefulness of our approach is validated by computational results.

cs.DS↗

arXiv2005

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 mainly on the number of em 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 the 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.

cs.DS↗

arXiv2005

Defragmenting the Module Layout of a Partially Reconfigurable Device

Modern generations of field-programmable gate arrays (FPGAs) allow for partial reconfiguration. In an online context, where the sequence of modules to be loaded on the FPGA is unknown beforehand, repeated insertion and deletion of modules leads to progressive fragmentation of the available space, making defragmentation an important issue. We address this problem by propose an online and an offline component for the defragmentation of the available space. We consider defragmenting the module layout on a reconfigurable device. This corresponds to solving a two-dimensional strip packing problem. Problems of this type are NP-hard in the strong sense, and previous algorithmic results are rather limited. Based on a graph-theoretic characterization of feasible packings, we develop a method that can solve two-dimensional defragmentation instances of practical size to optimality. Our approach is validated for a set of benchmark instances.

cs.AR↗

arXiv2005

A Practical Approach for Circuit Routing on Dynamic Reconfigurable Devices

Management of communication by on-line routing in new FPGAs with a large amount of logic resources and partial reconfigurability is a new challenging problem. A Network-on-Chip (NoC) typically uses packet routing mechanism, which has often unsafe data transfers, and network interface overhead. In this paper, circuit routing for such dynamic NoCs is investigated, and a practical 1-dimensional network with an efficient routing algorithm is proposed and implemented. Also, this concept has been extended to the 2-dimensional case. The implementation results show the low area overhead and high performance of this network.

cs.AR↗

arXiv2005

Online Searching with Turn Cost

We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the well-studied linear-search problem. We describe a strategy that is guaranteed to find the object at a cost of at most 9*OPT + 2d, which has the optimal competitive ratio 9 with respect to OPT plus the minimum corresponding additive term. Our argument for upper and lower bound uses an infinite linear program, which we solve by experimental solution of an infinite series of approximating finite linear programs, estimating the limits, and solving the resulting recurrences. We feel that this technique is interesting in its own right and should help solve other searching problems. In particular, we consider the star search or cow-path problem with turn cost, where the hidden object is placed on one of m rays emanating from the original position of the searcher. For this problem we give a tight bound of (1+(2(m^m)/((m-1)^(m-1))) OPT + m ((m/(m-1))^(m-1) - 1) d. We also discuss tradeoff between the corresponding coefficients, and briefly consider randomized strategies on the line.

cs.DS↗

arXiv2005

Koordinatenfreies Lokationsbewusstsein (Localization without Coordinates)

Localization is one of the fundamental issues in sensor networks. It is almost always assumed that it must be solved by assigning coordinates to the nodes. This article discusses positioning algorithms from a theoretical, practical and simulative point of view, and identifies difficulties and limitations. Ideas for more abstract means of location awareness are presented and the resulting possible improvements for applications are shown. Nodes with certain topological or environmental properties are clustered, and the neighborhood structure of the clusters is modeled as a graph. Eines der fundamentalen Probleme in Sensornetzwerken besteht darin, ein Bewusstsein fuer die Position eines Knotens im Netz zu entwickeln. Dabei wird fast immer davon ausgegangen, dass dies durch die Zuweisung von Koordinaten zu erfolgen hat. In diesem Artikel wird auf theoretischer, praktischer und simulativer Ebene ein kritischer Blick auf entsprechende Verfahren geworfen, und es werden Grenzen aufgezeigt. Es wird ein Ansatz vorgestellt, mit dem in der Zukunft eine abstrakte Form von Lokationsbewusstsein etabliert werden kann, und es wird gezeigt, wie Anwendungen dadurch verbessert werden koennen. Er basiert auf einer graphenbasierten Modellierung des Netzes: Knoten mit bestimmten topologischen oder Umwelteigenschaften werden zu Clustern zusammengefasst, und Clusternachbarschaften dann als Graphen modelliert.

cs.DC↗

arXiv2005

Shawn: A new approach to simulating wireless sensor networks

We consider the simulation of wireless sensor networks (WSN) using a new approach. We present Shawn, an open-source discrete-event simulator that has considerable differences to all other existing simulators. Shawn is very powerful in simulating large scale networks with an abstract point of view. It is, to the best of our knowledge, the first simulator to support generic high-level algorithms as well as distributed protocols on exactly the same underlying networks.

cs.DC↗

arXiv2004

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.

cs.DS↗

arXiv2004

The one-round Voronoi game replayed

We consider the one-round Voronoi game, where player one (``White'', called ``Wilma'') places a set of n points in a rectangular area of aspect ratio r <=1, followed by the second player (``Black'', called ``Barney''), who places the same number of points. Each player wins the fraction of the board closest to one of his points, and the goal is to win more than half of the total area. This problem has been studied by Cheong et al., who showed that for large enough $n$ and r=1, Barney has a strategy that guarantees a fraction of 1/2+a, for some small fixed a. We resolve a number of open problems raised by that paper. In particular, we give a precise characterization of the outcome of the game for optimal play: We show that Barney has a winning strategy for n>2 and r>sqrt{2}/n, and for n=2 and r>sqrt{3}/2. Wilma wins in all remaining cases, i.e., for n>=3 and r<=sqrt{2}/n, for n=2 and r<=sqrt{3}/2, and for n=1. We also discuss complexity aspects of the game on more general boards, by proving that for a polygon with holes, it is NP-hard to maximize the area Barney can win against a given set of points by Wilma.

cs.CG↗