arXiv subjects

Sandor P. Fekete

Publications and source records attributed to Sandor P. Fekete.

At least 19 recordsLinked to original sources

arXiv2016

Lower Bounds for Graph Exploration Using Local Policies

We give lower bounds for various natural node- and edge-based local strategies for exploring a graph. We consider this problem both in the setting of an arbitrary graph as well as the abstraction of a geometric exploration of a space by a robot, both of which have been extensively studied. We consider local exploration policies that use time-of-last- visit or alternatively least-frequently-visited local greedy strategies to select the next step in the exploration path. Both of these strategies were previously considered by Cooper et al. (2011) for a scenario in which counters for the last visit or visit frequency are attached to the edges. In this work we consider the case in which the counters are associated with the nodes, which for the case of dual graphs of geometric spaces could be argued to be intuitively more natural and likely more efficient. Surprisingly, these alternate strategies give worst-case superpolynomial/ exponential time for exploration, whereas the least-frequently visited strategy for edges has a polynomially bounded exploration time, as shown by Cooper et al. (2011).

cs.CG↗

arXiv2015

Distributed Cohesive Control for Robot Swarms: Maintaining Good Connectivity in the Presence of Exterior Forces

We present a number of powerful local mechanisms for maintaining a dynamic swarm of robots with limited capabilities and information, in the presence of external forces and permanent node failures. We propose a set of local continuous algorithms that together produce a generalization of a Euclidean Steiner tree. At any stage, the resulting overall shape achieves a good compromise between local thickness, global connectivity, and flexibility to further continuous motion of the terminals. The resulting swarm behavior scales well, is robust against node failures, and performs close to the best known approximation bound for a corresponding centralized static optimization problem.

cs.RO↗

arXiv2015

A Parallel Distributed Strategy for Arraying a Scattered Robot Swarm

We consider the problem of organizing a scattered group of $n$ robots in two-dimensional space, with geometric maximum distance $D$ between robots. The communication graph of the swarm is connected, but there is no central authority for organizing it. We want to arrange them into a sorted and equally-spaced array between the robots with lowest and highest label, while maintaining a connected communication network. In this paper, we describe a distributed method to accomplish these goals, without using central control, while also keeping time, travel distance and communication cost at a minimum. We proceed in a number of stages (leader election, initial path construction, subtree contraction, geometric straightening, and distributed sorting), none of which requires a central authority, but still accomplishes best possible parallelization. The overall arraying is performed in $O(n)$ time, $O(n^2)$ individual messages, and $O(nD)$ travel distance. Implementation of the sorting and navigation use communication messages of fixed size, and are a practical solution for large populations of low-cost robots.

cs.RO↗

arXiv2014

Local Policies for Efficiently Patrolling a Triangulated Region by a Robot Swarm

We present and analyze methods for patrolling an environment with a distributed swarm of robots. Our approach uses a physical data structure - a distributed triangulation of the workspace. A large number of stationary "mapping" robots cover and triangulate the environment and a smaller number of mobile "patrolling" robots move amongst them. The focus of this work is to develop, analyze, implement and compare local patrolling policies. We desire strategies that achieve full coverage, but also produce good coverage frequency and visitation times. Policies that provide theoretical guarantees for these quantities have received some attention, but gaps have remained. We present: 1) A summary of how to achieve coverage by building a triangulation of the workspace, and the ensuing properties. 2) A description of simple local policies (LRV, for Least Recently Visited and LFV, for Least Frequently Visited) for achieving coverage by the patrolling robots. 3) New analytical arguments why different versions of LRV may require worst case exponential time between visits of triangles. 4) Analytical evidence that a local implementation of LFV on the edges of the dual graph is possible in our scenario, and immensely better in the worst case. 5) Experimental and simulation validation for the practical usefulness of these policies, showing that even a small number of weak robots with weak local information can greatly outperform a single, powerful robots with full information and computational capabilities.

cs.RO↗

arXiv2011

Wiselib: A Generic Algorithm Library for Heterogeneous Sensor Networks

One unfortunate consequence of the success story of wireless sensor networks (WSNs) in separate research communities is an ever-growing gap between theory and practice. Even though there is a increasing number of algorithmic methods for WSNs, the vast majority has never been tried in practice; conversely, many practical challenges are still awaiting efficient algorithmic solutions. The main cause for this discrepancy is the fact that programming sensor nodes still happens at a very technical level. We remedy the situation by introducing Wiselib, our algorithm library that allows for simple implementations of algorithms onto a large variety of hardware and software. This is achieved by employing advanced C++ techniques such as templates and inline functions, allowing to write generic code that is resolved and bound at compile time, resulting in virtually no memory or computation overhead at run time. The Wiselib runs on different host operating systems, such as Contiki, iSense OS, and ScatterWeb. Furthermore, it runs on virtual nodes simulated by Shawn. For any algorithm, the Wiselib provides data structures that suit the specific properties of the target platform. Algorithm code does not contain any platform-specific specializations, allowing a single implementation to run natively on heterogeneous networks. In this paper, we describe the building blocks of the Wiselib, and analyze the overhead. We demonstrate the effectiveness of our approach by showing how routing algorithms can be implemented. We also report on results from experiments with real sensor-node hardware.

cs.NI↗

arXiv2011

Minimum Covering with Travel Cost

Given a polygon and a visibility range, the Myopic Watchman Problem with Discrete Vision (MWPDV) asks for a closed path P and a set of scan points S, such that (i) every point of the polygon is within visibility range of a scan point; and (ii) path length plus weighted sum of scan number along the tour is minimized. Alternatively, the bicriteria problem (ii') aims at minimizing both scan number and tour length. We consider both lawn mowing (in which tour and scan points may leave P) and milling (in which tour, scan points and visibility must stay within P) variants for the MWPDV; even for simple special cases, these problems are NP-hard. We show that this problem is NP-hard, even for the special cases of rectilinear polygons and L_\infty scan range 1, and negligible small travel cost or negligible travel cost. For rectilinear MWPDV milling in grid polygons we present a 2.5-approximation with unit scan range; this holds for the bicriteria version, thus for any linear combination of travel cost and scan cost. For grid polygons and circular unit scan range, we describe a bicriteria 4-approximation. These results serve as stepping stones for the general case of circular scans with scan radius r and arbitrary polygons of feature size a, for which we extend the underlying ideas to a pi(r/a}+(r+1)/2) bicriteria approximation algorithm. Finally, we describe approximation schemes for MWPDV lawn mowing and milling of grid polygons, for fixed ratio between scan cost and travel cost.

cs.DS↗

arXiv2011

Disruption Management with Rescheduling of Trips and Vehicle Circulations

This paper introduces a combined approach for the recovery of a timetable by rescheduling trips and vehicle circulations for a rail-based transportation system subject to disruptions. We propose a novel event-based integer programming (IP) model. Features include shifting and canceling of trips as well as modifying the vehicle schedules by changing or truncating the circulations. The objective maximizes the number of recovered trips, possibly with delay, while guaranteeing a conflict-free new timetable for the estimated time window of the disruption. We demonstrate the usefulness of our approach through experiments for real-life test instances of relevant size, arising from the subway system of Vienna. We focus on scenarios in which one direction of one track is blocked, and trains have to be scheduled through this bottleneck. Solving these instances is made possible by contracting parts of the underlying event-activity graph; this allows a significant size reduction of the IP. Usually, the solutions found within one minute are of good quality and can be used as good estimates of recovery plans in an online context.

math.OC↗

arXiv2010

A Protocol for Self-Synchronized Duty-Cycling in Sensor Networks: Generic Implementation in Wiselib

In this work we present a protocol for self-synchronized duty-cycling in wireless sensor networks with energy harvesting capabilities. The protocol is implemented in Wiselib, a library of generic algorithms for sensor networks. Simulations are conducted with the sensor network simulator Shawn. They are based on the specifications of real hardware known as iSense sensor nodes. The experimental results show that the proposed mechanism is able to adapt to changing energy availabilities. Moreover, it is shown that the system is very robust against packet loss.

cs.AI↗

arXiv2010

Online Square Packing

We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0,1] that arrive from above, one at a time. The objective is to pack these items as they arrive, minimizing the resulting height. Just like in the classical game of Tetris, each square must be moved along a collision-free path to its final destination. In addition, we account for gravity in both motion (squares must never move up) and position (any final destination must be supported from below). A similar problem has been considered before; the best previous result is by Azar and Epstein, who gave a 4-competitive algorithm in a setting without gravity (i.e., with the possibility of letting squares "hang in the air") based on ideas of shelf-packing: Squares are assigned to different horizontal levels, allowing an analysis that is reminiscent of some bin-packing arguments. We apply a geometric analysis to establish a competitive factor of 3.5 for the bottom-left heuristic and present a 34/13=2.615...-competitive algorithm.

cs.DS↗

arXiv2010

Simultaneous Event Execution in Heterogeneous Wireless Sensor Networks

We present a synchronization algorithm to let nodes in a sensor network simultaneously execute a task at a given point in time. In contrast to other time synchronization algorithms we do not provide a global time basis that is shared on all nodes. Instead, any node in the network can spontaneously initiate a process that allows the simultaneous execution of arbitrary tasks. We show that our approach is beneficial in scenarios where a global time is not needed, as it requires little communication compared with other time synchronization algorithms. We also show that our algorithm works in heterogeneous systems where the hardware provides highly varying clock accuracy. Moreover, heterogeneity does not only affect the hardware, but also the communication channels. We deal with different connection types---from highly unreliable and fluctuating wireless channels to reliable and fast wired connections.

cs.DC↗

arXiv2010

Integer Point Sets Minimizing Average Pairwise L1-Distance: What is the Optimal Shape of a Town?

An n-town, for a natural number n, is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town has optimal shape if the sum of all pairwise Manhattan distances is minimized. This problem has been studied for cities, i.e., the limiting case of very large n. For cities, it is known that the optimal shape can be described by a differential equation, for which no closed-form is known. We show that optimal n-towns can be computed in O(n^7.5) time. This is also practically useful, as it allows us to compute optimal solutions up to n=80.

cs.CG↗

arXiv2010

Polygon Exploration with Time-Discrete Vision

With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of useful accuracy does not allow the robot to scan continuously while in motion; instead, it has to stop each time it surveys its environment. This requirement was studied by Fekete, Klein and Nuechter for the subproblem of looking around a corner, but until now has not been considered in an online setting for whole polygonal regions. We give the first algorithmic results for this important algorithmic problem that combines stationary art gallery-type aspects with watchman-type issues in an online scenario: We demonstrate that even for orthoconvex polygons, a competitive strategy can be achieved only for limited aspect ratio A (the ratio of the maximum and minimum edge length of the polygon), i.e., for a given lower bound on the size of an edge; we give a matching upper bound by providing an O(log A)-competitive strategy for simple rectilinear polygons, using the assumption that each edge of the polygon has to be fully visible from some scan point.

cs.CG↗

arXiv2010

Hallway Monitoring: Distributed Data Processing with Wireless Sensor Networks

We present a sensor network testbed that monitors a hallway. It consists of 120 load sensors and 29 passive infrared sensors (PIRs), connected to 30 wireless sensor nodes. There are also 29 LEDs and speakers installed, operating as actuators, and enabling a direct interaction between the testbed and passers-by. Beyond that, the network is heterogeneous, consisting of three different circuit boards---each with its specific responsibility. The design of the load sensors is of extremely low cost compared to industrial solutions and easily transferred to other settings. The network is used for in-network data processing algorithms, offering possibilities to develop, for instance, distributed target-tracking algorithms. Special features of our installation are highly correlated sensor data and the availability of miscellaneous sensor types.

cs.DC↗

arXiv2010

Circle Packing for Origami Design Is Hard

We show that deciding whether a given set of circles can be packed into a rectangle, an equilateral triangle, or a unit square are NP-hard problems, settling the complexity of these natural packing problems. On the positive side, we show that any set of circles of total area 1 can be packed into a square of size 4/\sqrt{pi}=2.2567... These results are motivated by problems arising in the context of origami design.

cs.CG↗

arXiv2010

Evacuation of rectilinear polygons

We investigate the problem of creating fast evacuation plans for buildings that are modeled as grid polygons, possibly containing exponentially many cells. We study this problem in two contexts: the ``confluent'' context in which the routes to exits remain fixed over time, and the ``non-confluent'' context in which routes may change. Confluent evacuation plans are simpler to carry out, as they allocate contiguous regions to exits; non-confluent allocation can possibly create faster evacuation plans. We give results on the hardness of creating the evacuation plans and strongly polynomial algorithms for finding confluent evacuation plans when the building has two exits. We also give a pseudo-polynomial time algorithm for non-confluent evacuation plans. Finally, we show that the worst-case bound between confluent and non-confluent plans is 2-2/(k+1).

cs.DS↗

arXiv2010

Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.

cs.CG↗

arXiv2010

Maintaining Virtual Areas on FPGAs using Strip Packing with Delays

Every year, the computing resources available on dynamically partially reconfigurable devices increase enormously. In the near future, we expect many applications to run on a single reconfigurable device. In this paper, we present a concept for multitasking on dynamically partially reconfigurable systems called virtual area management. We explain its advantages, show its challenges, and discuss possible solutions. Furthermore, we investigate one problem in more detail: Packing modules with time-varying resource requests. This problem from the reconfigurable computing field results in a completely new optimization problem not tackled before. ILP-based and heuristic approaches are compared in an experimental study and the drawbacks and benefits discussed.

cs.AR↗

arXiv2008

Minimizing the stabbing number of matchings, trees, and triangulations

The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or triangulations of minimum stabbing number for a given set of points. The complexity of these problems has been a long-standing open question; in fact, it is one of the original 30 outstanding open problems in computational geometry on the list by Demaine, Mitchell, and O'Rourke. The answer we provide is negative for a number of minimum stabbing problems by showing them NP-hard by means of a general proof technique. It implies non-trivial lower bounds on the approximability. On the positive side we propose a cut-based integer programming formulation for minimizing the stabbing number of matchings and spanning trees. We obtain lower bounds (in polynomial time) from the corresponding linear programming relaxations, and show that an optimal fractional solution always contains an edge of at least constant weight. This result constitutes a crucial step towards a constant-factor approximation via an iterated rounding scheme. In computational experiments we demonstrate that our approach allows for actually solving problems with up to several hundred points optimally or near-optimally.

cs.CG↗