Algorithms for Sensor Systems: 6th International Workshop on Algorithms for Sensor Systems, Wireless Ad Hoc Networks, and Autonomous Mobile Entities, ALGOSENSORS 2010, Bordeaux, France, July 5, 2010, Revised Selected Papers

197 Pages·2010·2.81 MB·English

by  Iyad A. Kanj

Lecture Notes in Computer Science 6451
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Christian Scheideler (Ed.)
Algorithms
for Sensor Systems
6th International Workshop on Algorithms
forSensorSystems,WirelessAdHocNetworks,
and Autonomous Mobile Entities
ALGOSENSORS 2010
Bordeaux, France, July 5, 2010
Revised Selected Papers
1 3
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DepartmentofComputerScience
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ISBN-10 3-642-16987-2SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-642-16987-8SpringerBerlinHeidelbergNewYork
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Preface
This volume contains the papers presented at ALGOSENSORS 2010, the 6th
International Workshop on Algorithms for Sensor Systems, Wireless Ad Hoc
Networks and Autonomous Mobile Entities, held on July 5, 2010 in Bordeaux,
France.
There were 31 submissions. Each submission was reviewed by four Program
Committee members. The committee decided to accept 15 papers, among them
two brief announcements.
TheProgramCommitteewouldliketothankallwhosubmittedpapersandall
the external reviewerswho helped us evaluate the submissions. As the Program
Chair of ALGOSENSORS 2010, I would like to express my deep gratitude to
the Program Committee for all of their work during the paper review process
andthefruitfuldiscussions.IwouldalsoliketothanktheWorkshopsChairRalf
Klasing for organizing a wonderful workshop in Bordeaux.
July 2010 Christian Scheideler
Conference Organization
Program Chair
Christian Scheideler University of Paderborn, Germany
Program Committee
Matthew Andrews Bell Laboratories,USA
Novella Bartolini University of Rome “La Sapienza,” Italy
Prosenjit Bose Carleton University, Canada
Ioannis Caragiannis University of Patras, Greece
Bogdan Chlebus University of Colorado Denver, USA
Sa´ndor Fekete Braunschweig University of Technology,
Germany
Hannes Frey University of Paderborn, Germany
Jie Gao SUNY Stony Brook, USA
Ralf Klasing CNRS & University of Bordeaux (LaBRI)
& INRIA, France
Miroslaw Korzeniowski Wroclaw University of Technology, Poland
Pierre Leone University of Geneva, Switzerland
Xu Li University of Ottawa, Canada
Zvi Lotker Ben-Gurion University of the Negev, Israel
Alberto Marchetti-Spaccamela University of Rome “La Sapienca,” Italy
Thomas Moscibroda Microsoft Research, USA
Pekka Orponen Aalto University, Finland
Victor Prasanna University of Southern California, USA
Liam Roditty Bar-Ilan University, Israel
Paolo Santi CNR, Italy
Gabriel Scalosub Ben-Gurion University of the Negev, Israel
Christian Schindelhauer University of Freiburg, Germany
Stefan Schmid Deutsche Telekom Laboratories,Germany
Berthold Vo¨cking RWTH Aachen, Germany
Local Arrangements
Ralf Klasing CNRS & University of Bordeaux (LaBRI)
& INRIA, France
VIII Conference Organization
External Reviewers
Nicolas Bonichon Thomas Kesselheim
Michael Borokhovich Marek Klonowski
Shiri Chechick Luca Moscardelli
Mohammad Farshi Animesh Pathak
Maciek Gabala Andrzej Pelc
Lee-Ad Gottlieb Hanan Shpungin
David Ilcinkas Simone Silvestri
Artur Jez Marcin Zawada
Table of Contents
Improved Local Algorithms for Spanner Construction................. 1
Iyad A. Kanj and Ge Xia
Planar Hop Spanners for Unit Disk Graphs.......................... 16
Nicolas Catusse, Victor Chepoi, and Yann Vax`es
Brief Announcement: Hierarchical Neighbor Graphs: A Sparse
Connected Structure for Euclidean Point Sets ....................... 31
Amitabha Bagchi, Adit Madan, and Achal Premi
Minimum Energy Broadcast on Rectangular Grid Wireless Networks ... 34
Atsushi Murata and Akira Matsubayashi
Scheduling Multicast Transmissions under SINR Constraints .......... 47
Thomas Erlebach and Tom Grant
Deterministic Recurrent Communication and Synchronization in
Restricted Sensor Networks ....................................... 62
Antonio Fern´andez Anta, Miguel A. Mosteiro, and
Christopher Thraves
k+ Decision Trees (Extended Abstract)............................. 74
James Aspnes, Eric Blais, Murat Demirbas, Ryan O’Donnell,
Atri Rudra, and Steve Uurtamo
Brief Announcement: Regional Consecutive Leader Election in Mobile
Ad-Hoc Networks ................................................ 89
Hyun Chul Chung, Peter Robinson, and Jennifer L. Welch
From Key Predistribution to Key Redistribution ..................... 92
Jacek Cichon´, Zbigniew Go(cid:2)le¸biewski, and Miros(cid:2)law Kutyl(cid:2)owski
In-networkCoding for ResilientSensor Data StorageandEfficientData
Mule Collection.................................................. 105
Michele Albano and Jie Gao
Monitoring Churn in Wireless Networks ............................ 118
Stephan Holzer, Yvonne Anne Pignolet, Jasmin Smula, and
Roger Wattenhofer
Lifetime Maximization of Monitoring Sensor Networks................ 134
Peter Sanders and Dennis Schieferdecker
MSDR-D Network Localization Algorithm .......................... 148
Kevin Coogan, Varun Khare, Stephen G. Kobourov, and
Bastian Katz
X Table of Contents
Virtual Raw Anchor Coordinates: A New Localization Paradigm....... 161
Florian Huc, Aubin Jarry, Pierre Leone, and Jos´e Rolim
Self-localization Based on Ambient Signals .......................... 176
Thomas Janson, Christian Schindelhauer, and Johannes Wendeberg
Author Index.................................................. 189
Improved Local Algorithms for Spanner
Construction
Iyad A. Kanj1 and Ge Xia2
1 School of Computing, DePaul University,243 S. Wabash Avenue,
Chicago, IL 60604, USA
[email protected]
2 Department of Computer Science, Acopian Engineering Center,
Lafayette College, Easton PA 18042, USA
[email protected]
Abstract. Let S be a set of n points in the plane, let E be the com-
plete Euclidean graph whose point-set is S, and let G be the Delaunay
triangulation of S. We present a very simple local algorithm that, given
G, constructs a subgraph of G of degree at most 11 that is a geometric
spannerof Gwith stretch factor 2.86, andhenceageometric spannerof
E with stretch factor < 7. This algorithm gives an O(nlgn) time cen-
tralized algorithm for constructing a subgraph of G that is a geometric
spanner of E of degree at most 11 and stretch factor <7.
The algorithm can be generalized to unit disk graphs to give a local
algorithmforconstructingaplanespannerofaunitdiskgraphofdegree
at most 11 and stretch factor <7.
Keywords: spanners, Delaunay triangulations, unit disk graphs.
1 Introduction
LetS be a setofpoints inthe plane,andletE be the complete Euclideangraph
whose point-set is S. It is well known that the Delaunay triangulation G of S
is a plane geometric (i.e., with respect to the Euclidean distance) spanner of E
with stretch factor Cdel <2.42 [13].
In this paper we consider the problem of constructing a bounded-degree sub-
graph of G that is a spanner of G under the local model of computation. The
motivation behind these requirements stems from applications in wireless ad-
hoc and sensor networks. In such applications plane spanners are used as the
underlying topologies for efficient unicasting, multicasting, and broadcasting
(see[4,5,10,14,15,17,19]).Theboundeddegreerequirementisimportantformin-
imizinginterferenceamongthewirelessdevicesinthenetwork.Asuitablemodel
of computation for such systems is the local model, in which the computation
performed by each device only depends on the information available within its
neighborhood. More formally, a local algorithm is a distributed algorithm that
can be simulated to run in a constant number of synchronous communication
rounds [18].
C.Scheideler(Ed.):ALGOSENSORS2010,LNCS6451,pp.1–15,2010.
(cid:2)c Springer-VerlagBerlinHeidelberg2010
2 I.A. Kanj and G. Xia
Under the centralized model of computation, the problem of constructing a
bounded-degreesubgraphofGthatisaspannerhasreceivedsignificantinterest.
Bose et al. [3,4] were the first to show how to extract a subgraph of G that
is a spanner of E with degree at most 27 and stretch factor 10.02. Bose et
al. [7] then improved the aforementioned result and showed how to construct
a subgraph of G that is a spanner of E with degree at most 17 and stretch
factor 23. This result was subsequently improved by Kanj and Perkovi´c [11]
who presented an algorithm that constructs a subgraph of G with degree at
most 14 and stretch factor 3.54 (w.r.t. E).1 Very recently (unpublished), Carmi
and Chaitman [8] were able to improve Kanj and Perkovi´c’s result further by
presenting an algorithm t√hat computes a subgraph of G with degree at most
7 and stretch factor (1+ 2)2 ·Cdel < 14.1. Carmi and Chaitman’s result [8]
can be extended to the distributed model of computation to yield a distributed
algorithmthatcomputes asubgraphofGofdegreeatmost7andstretchfactor
14.1; however, their algorithm is inherently nonlocal. All the aforementioned
centralized algorithms run in O(n) time when G is given as input, and in time
O(nlgn) otherwise (n = |S|). We note that, very recently, a spanner of E of
degree atmost 6 andstretch factor 6 was givenin [2]. This spanner,however,is
not a subgraph of G.
Computing a subgraph of G of minimum degree that is a spanner is a very
challenging open problem in computational geometry (for example, see the re-
centsurveybyBoseandSmid[6]).Therefore,itbecomeschallengingtocompute
a subgraph of G of “small degree” that is a spanner. The problem, of course,
becomes even more challenging if we restrict ourselves to local algorithms, due
to the strict limitations imposed by the local model of computation. As a mat-
ter of fact, under the local model of computation, we are only aware of Kanj
and Perkovi´c’sresult [11], which gives the first local algorithm that computes a
subgraph of G of degree at most 14 and stretch factor 3.54.
In this paper we make some progress towards solving the aforementioned
problem. We present a very simple local algorithm that constructs a subgraph
of G of degree at most 11 and stretch factor 2.86 with respect to G, and hence
stretchfactor2.86·Cdel <7withrespecttoE.Thealgorithmcanbeimplemented
torunin2synchronouscommunicationrounds(i.e.,thelocalityis2).Toputthe
result of this paper in context, this result improves the local algorithm of Kanj
and Perkovi´c [11] in terms of the minimum degree bound achieved (11 versus
14).Moreover,thealgorithmpresentedinthecurrentpaperissimplerthanthat
in [11].
The local algorithm presented in this paper can be implemented to run in
O(n) time under the centralized model when G is given, and in O(nlgn) time
otherwise.
Wenotethatinwirelesscomputingthenetworkisoftenmodeledasaunitdisk
graph (UDG) rather than a complete Euclidean graph. Many of the algorithms
mentioned above (among others) can be modified to construct bounded-degree
plane spanners of UDGs [3,4,11,12] (see also [19]). The results in this paper can
1 A journal version of theresults in [11] appears in [12] (with G. Xia).