Distributed algorithms for overlay networks and programmable matter

This dissertation consists of two parts that are dedicated to the study of distributed algorithms for overlay networks and programmable matter. The first part revolves around the topics of robustness against attacks, recovery from faults, and monitoring network properties in the context of overlay networks. More specifically, we introduce network protocols that maintain the connectivity of an overlay network under massive adversarial churn or denial-of-service attacks, we present a self-stabilizing algorithm for the construction of metric graphs, and we initiate the study of hybrid networks by investigating the problem of continuously monitoring properties of an externally-controlled network with the help of an overlay network. In the second part we investigate the algorithmic foundations of programmable matter. Programmable matter refers to a substance that can change its shape or other physical properties in a programmable fashion. We envision programmable matter consisting of simple computational devices that are able to self-organize in order to achieve a collective goal without any central control or external intervention. We present efficient algorithms for the fundamental problems of leader election and shape formation for programmable matter.

[1]  Joseph JáJá,et al.  An Introduction to Parallel Algorithms , 1992 .

[2]  T. Nakagaki,et al.  Intelligence: Maze-solving by an amoeboid organism , 2000, Nature.

[3]  Christian Scheideler,et al.  Linearization: Locally Self-Stabilizing Sorting in Graphs , 2007, ALENEX.

[4]  Roger Wattenhofer,et al.  Tight bounds for distributed selection , 2007, SPAA '07.

[5]  Gopal Pandurangan.  Distributed Algorithmic Foundations of Dynamic Networks , 2014, SIROCCO.

[6]  Damien Woods,et al.  Intrinsic universality and the computational power of self-assembly , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Nicola Santoro,et al.  Arbitrary pattern formation by asynchronous, anonymous, oblivious robots , 2008, Theor. Comput. Sci..

[8]  Kurt Mehlhorn,et al.  Physarum can compute shortest paths , 2011, SODA.

[9]  Matthew J. Patitz.  An introduction to tile-based self-assembly and a survey of recent results , 2014, Natural Computing.

[10]  Chryssis Georgiou,et al.  A distributed algorithm for gathering many fat mobile robots in the plane , 2013, PODC '13.

[11]  Christian Scheideler,et al.  Improved Leader Election for Self-organizing Programmable Matter , 2017, ALGOSENSORS.

[12]  Christian Scheideler,et al.  Universal coating for programmable matter , 2016, Theor. Comput. Sci..

[13]  M. Sahani,et al.  Algorithmic Self-Assembly of DNA , 2006 .

[14]  Yukiko Yamauchi,et al.  Brief Announcement: Shape Formation by Programmable Particles , 2017, DISC.

[15]  Nick Mathewson,et al.  Tor: The Second-Generation Onion Router , 2004, USENIX Security Symposium.

[16]  Christian Scheideler,et al.  IRIS: a robust information system against insider dos-attacks , 2013, SPAA.

[17]  Felix C. Gaertner,et al.  A Survey of Self-Stabilizing Spanning-Tree Construction Algorithms , 2003 .

[18]  Aristides A. G. Requicha,et al.  Self-assembly and self-repair of arbitrary shapes by a swarm of reactive robots: algorithms and simulations , 2010, Auton. Robots.

[19]  Stefan Schmid,et al.  A Self-repairing Peer-to-Peer System Resilient to Dynamic Adversarial Churn , 2005, IPTPS.

[20]  Mikhail J. Atallah,et al.  Finding Euler Tours in Parallel , 2011, J. Comput. Syst. Sci..

[21]  Christian Scheideler,et al.  Tiara: A self-stabilizing deterministic skip list and skip graph , 2012, Theor. Comput. Sci..

[22]  Revathi Ananthakrishnan,et al.  The Forces Behind Cell Movement , 2007, International journal of biological sciences.

[23]  Fabian Kuhn,et al.  On the power of the congested clique model , 2014, PODC.

[24]  Tommaso Toffoli,et al.  Programmable Matter: Concepts and Realization , 1993, Int. J. High Speed Comput..

[25]  Michael Elkin,et al.  Unconditional lower bounds on the time-approximation tradeoffs for the distributed minimum spanning tree problem , 2004, STOC '04.

[26]  Damien Woods,et al.  Parallel computation using active self-assembly , 2014, Natural Computing.

[27]  Peter Robinson,et al.  DEX: Self-Healing Expanders , 2014, IPDPS.

[28]  James Aspnes,et al.  The expansion and mixing time of skip graphs with applications , 2005, SPAA '05.

[29]  Yossi Azar,et al.  A generic scheme for building overlay networks in adversarial scenarios , 2003, Proceedings International Parallel and Distributed Processing Symposium.

[30]  Angelos D. Keromytis,et al.  SOS: secure overlay services , 2002, SIGCOMM '02.

[31]  Christian Scheideler,et al.  Re-Chord: a self-stabilizing chord overlay network , 2011, SPAA.

[32]  Lila Kari,et al.  DNA Computing: Models and Implementations , 2002 .

[33]  Emanuele Viola,et al.  On the Complexity of Information Spreading in Dynamic Networks , 2013, SODA.

[34]  Gregory S. Chirikjian,et al.  Kinematics of a metamorphic robotic system , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[35]  Michael J. Fischer,et al.  Computation in networks of passively mobile finite-state sensors , 2004, PODC '04.

[36]  Boaz Patt-Shamir,et al.  Minimum-Weight Spanning Tree Construction in O(log log n) Communication Rounds , 2005, SIAM J. Comput..

[37]  Dana Randall,et al.  A Stochastic Approach to Shortcut Bridging in Programmable Matter , 2017, DNA.

[38]  Christian Scheideler,et al.  Self-Stabilizing De Bruijn Networks , 2011, SSS.

[39]  Esther M. Arkin,et al.  Algorithms for Rapidly Dispersing Robot Swarms in Unknown Environments , 2002, WAFR.

[40]  Seth Copen Goldstein,et al.  Programmable Matter , 2005, Computer.

[41]  Christian Schindelhauer,et al.  Distributed random digraph transformations for peer-to-peer networks , 2006, SPAA '06.

[42]  Dan Alistarh,et al.  Polylogarithmic-Time Leader Election in Population Protocols , 2015, ICALP.

[43]  Ronitt Rubinfeld,et al.  Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time , 2005, SIAM J. Comput..

[44]  Nei Kato,et al.  THUP: A P2P Network Robust to Churn and DoS Attack Based on Bimodal Degree Distribution , 2013, IEEE Journal on Selected Areas in Communications.

[45]  James McLurkin,et al.  Analysis and implementation of distributed algorithms for multi-robot systems , 2008 .

[46]  John R. Douceur,et al.  The Sybil Attack , 2002, IPTPS.

[47]  Kai-Yeung Siu,et al.  Distributed construction of random expander networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[48]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Thomas Locher,et al.  Foundations of aggregation and synchronization in distributed systems , 2009 .

[50]  Paul G. Spirakis,et al.  Simple and efficient local codes for distributed stable network construction , 2013, Distributed Computing.

[51]  Prasad Tetali,et al.  Distributed Random Walks , 2013, JACM.

[52]  David Doty,et al.  Theory of algorithmic self-assembly , 2012, CACM.

[53]  Christian Scheideler,et al.  Universal Shape Formation for Programmable Matter , 2016, SPAA.

[54]  Christian Scheideler,et al.  A denial-of-service resistant DHT , 2007, PODC '07.

[55]  Bernard Chazelle,et al.  Natural algorithms , 2009, SODA.

[56]  Nancy A. Lynch,et al.  Distributed computation in dynamic networks , 2010, STOC '10.

[57]  Uri Zwick,et al.  Optimal randomized EREW PRAM algorithms for finding spanning forests and for other basic graph connectivity problems , 1996, SODA '96.

[58]  Andrew Berns,et al.  Building self-stabilizing overlay networks with the transitive closure framework , 2011, Theor. Comput. Sci..

[59]  L. Asz.  Random Walks on Graphs: a Survey , 2022 .

[60]  Ho-Lin Chen,et al.  Fast Algorithmic Self-assembly of Simple Shapes Using Random Agitation , 2014, DNA.

[61]  Jared Saia,et al.  Picking up the Pieces: Self-Healing in reconfigurable networks , 2008, 2008 IEEE International Symposium on Parallel and Distributed Processing.

[62]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

[63]  Amin Saberi,et al.  A Local Switch Markov Chain on Given Degree Graphs with Application in Connectivity of Peer-to-Peer Networks , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[64]  Mitsunori Ogihara,et al.  Simulating Boolean circuits on a DNA computer , 1997, RECOMB '97.

[65]  Mark Braverman,et al.  On the convergence of the Hegselmann-Krause system , 2012, ITCS '13.

[66]  Dana Randall,et al.  A Markov Chain Algorithm for Compression in Self-Organizing Particle Systems , 2016, PODC.

[67]  Danupon Nanongkai,et al.  Fast distributed random walks , 2009, PODC '09.

[68]  Gopal Pandurangan,et al.  Stochastic analysis of a churn-tolerant structured peer-to-peer scheme , 2010, Peer-to-Peer Networking and Applications.

[69]  Antony I. T. Rowstron,et al.  Pastry: Scalable, Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems , 2001, Middleware.

[70]  Christian Scheideler,et al.  Churn- and DoS-resistant Overlay Networks Based on Network Reconfiguration , 2016, SPAA.

[71]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[72]  Christian Scheideler,et al.  A distributed polylogarithmic time algorithm for self-stabilizing skip graphs , 2009, PODC '09.

[73]  Sriram V. Pemmaraju,et al.  Toward Optimal Bounds in the Congested Clique: Graph Connectivity and MST , 2015, PODC.

[74]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[75]  Christian Scheideler,et al.  Towards Scalable and Robust Overlay Networks , 2007, IPTPS.

[76]  Carl Gutwin,et al.  Classes of graphs which approximate the complete euclidean graph , 1992, Discret. Comput. Geom..

[77]  Christian Scheideler,et al.  On Stabilizing Departures in Overlay Networks , 2014, SSS.

[78]  Li Gong,et al.  Industry Report: JXTA: A Network Programming Environment , 2001, IEEE Internet Comput..

[79]  Thomas Fuhrmann,et al.  Self-Stabilizing Ring Networks on Connected Graphs , 2005 .

[80]  Nicola Santoro,et al.  Mediated Population Protocols: Leader Election and Applications , 2017, TAMC.

[81]  Alon Itai,et al.  Symmetry breaking in distributed networks , 1990, Inf. Comput..

[82]  Joel Friedman,et al.  A proof of Alon's second eigenvalue conjecture and related problems , 2004, ArXiv.

[83]  Shay Kutten,et al.  Time Optimal Self-Stabilizing Spanning Tree Algorithms , 1993, FSTTCS.

[84]  David Peleg,et al.  A near-tight lower bound on the time complexity of distributed MST construction , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[85]  Douglas S. Reeves,et al.  Self-stabilizing structured ring topology P2P systems , 2005, Fifth IEEE International Conference on Peer-to-Peer Computing (P2P'05).

[86]  Christian Scheideler,et al.  RoBuSt: A Crash-Failure-Resistant Distributed Storage System , 2014, OPODIS.

[87]  Edsger W. Dijkstra,et al.  Self-stabilizing systems in spite of distributed control , 1974, CACM.

[88]  P. Rothemund.  Folding DNA to create nanoscale shapes and patterns , 2006, Nature.

[89]  Atul Singh,et al.  Eclipse Attacks on Overlay Networks: Threats and Defenses , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[90]  Petra Berenbrink,et al.  Estimating the number of connected components in sublinear time , 2014, Inf. Process. Lett..

[91]  Christoph Lenzen,et al.  Optimal deterministic routing and sorting on the congested clique , 2012, PODC '13.

[92]  James Aspnes,et al.  Fast construction of overlay networks , 2005, SPAA '05.

[93]  Carl Gutwin,et al.  The Delauney Triangulation Closely Approximates the Complete Euclidean Graph , 1989, WADS.

[94]  Peter Robinson,et al.  Fast Distributed Algorithms for Connectivity and MST in Large Graphs , 2015, SPAA.

[95]  David Soloveichik,et al.  Stable Leader Election in Population Protocols Requires Linear Time , 2015, DISC.

[96]  Joel L. Schiff,et al.  Cellular Automata: A Discrete View of the World (Wiley Series in Discrete Mathematics & Optimization) , 2007 .

[97]  Christian Scheideler,et al.  On the runtime of universal coating for programmable matter , 2016, Natural Computing.

[98]  Stefan Schmid,et al.  Distributed computation of the mode , 2008, PODC '08.

[99]  Othon Michail,et al.  Terminating distributed construction of shapes and patterns in a fair solution of automata , 2015, Distributed Computing.

[100]  Christian Scheideler,et al.  Distributed Monitoring of Network Properties: The Power of Hybrid Networks , 2017, ICALP.

[101]  Nicola Santoro,et al.  On the computational power of oblivious robots: forming a series of geometric patterns , 2010, PODC '10.

[102]  Robert E. Tarjan,et al.  An Efficient Parallel Biconnectivity Algorithm , 2011, SIAM J. Comput..

[103]  Christian Scheideler,et al.  Self-stabilizing Metric Graphs , 2016, SSS.

[104]  Friedhelm Meyer auf der Heide,et al.  Continuous Aggregation in Dynamic Ad-Hoc Networks , 2014, SIROCCO.

[105]  Reuven Cohen,et al.  Local spreading algorithms for autonomous robot systems , 2008, Theor. Comput. Sci..

[106]  E. Shapiro,et al.  Programmable and autonomous computing machine made of biomolecules , 2001, Nature.

[107]  Hagit Attiya,et al.  Distributed Computing: Fundamentals, Simulations and Advanced Topics , 1998 .

[108]  Artur Czumaj,et al.  Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time , 2009, SIAM J. Comput..

[109]  Christoph Lenzen,et al.  Algebraic methods in the congested clique , 2015, Distributed Computing.

[110]  Thomas P. Hayes,et al.  The forgiving graph: a distributed data structure for low stretch under adversarial attack , 2009, PODC.

[111]  Ben Y. Zhao,et al.  Tapestry: a resilient global-scale overlay for service deployment , 2004, IEEE Journal on Selected Areas in Communications.

[112]  David R. Karger,et al.  Faster information dissemination in dynamic networks via network coding , 2011, PODC '11.

[113]  Martin E. Dyer,et al.  The flip markov chain and a randomising P2P protocol , 2009, PODC '09.

[114]  Ke Li,et al.  Slime Mold Inspired Path Formation Protocol for Wireless Sensor Networks , 2010, ANTS Conference.

[115]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[116]  Bernard Chazelle,et al.  Approximating the Minimum Spanning Tree Weight in Sublinear Time , 2001, ICALP.

[117]  Nicola Santoro,et al.  Distributed Computing by Mobile Robots: Gathering , 2012, SIAM J. Comput..

[118]  Zack J. Butler,et al.  Generic Decentralized Control for Lattice-Based Self-Reconfigurable Robots , 2004, Int. J. Robotics Res..

[119]  Erik Winfree,et al.  Active self-assembly of algorithmic shapes and patterns in polylogarithmic time , 2013, ITCS '13.

[120]  Radhika Nagpal,et al.  Programmable self-assembly in a thousand-robot swarm , 2014, Science.

[121]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[122]  G. Church,et al.  Synthetic Gene Networks That Count , 2009, Science.

[123]  Christian Scheideler,et al.  Towards higher-dimensional topological self-stabilization: A distributed algorithm for Delaunay graphs , 2012, Theor. Comput. Sci..