Structures and Algorithms for the Collaboration between Peers and their Application in Solipsis

This report proposes a promising solution for constructing scalable p2p networks based on the 3D Delaunay Triangulation (DT). The key idea of the design is to maintain for each node a DT of the neighbour nodes. While demonstrating scalability in a real system is not practical for the current work, we demonstrate the scalability of the 3D DT using simulation. The results obtained indicate that there are upper bounds on the time needed to join and on the average number of neighbours maintained by a peer. Therefore, the amount of bandwidth and processing requirement for each node is bound, independent of the total number of nodes in the system.

[1]  Michael Ian Shamos,et al.  Closest-point problems , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[2]  Gwendal Simon,et al.  Solipsis: A Massively Multi-Participant Virtual World , 2003, PDPTA.

[3]  Olivier Devillers,et al.  Walking in a triangulation , 2001, SCG '01.

[4]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[5]  Steven Fortune,et al.  A sweepline algorithm for Voronoi diagrams , 1986, SCG '86.

[6]  Luís E. T. Rodrigues,et al.  GeoPeer: a location-aware peer-to-peer system , 2004, Third IEEE International Symposium on Network Computing and Applications, 2004. (NCA 2004). Proceedings..

[7]  Mariette Yvinec,et al.  Programming with CGAL: the example of triangulations , 1999, SCG '99.

[8]  Jonathan Richard Shewchuk,et al.  Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates , 1997, Discret. Comput. Geom..

[9]  Georges Voronoi.  Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .

[10]  Mariette Yvinec,et al.  Algorithmic geometry , 1998 .

[11]  Franz Aurenhammer,et al.  Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.

[12]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[13]  Miguel Castro,et al.  Scribe: a large-scale and decentralized application-level multicast infrastructure , 2002, IEEE J. Sel. Areas Commun..

[14]  Andy Oram,et al.  Peer-to-Peer: Harnessing the Power of Disruptive Technologies , 2001 .

[15]  R. Prim.  Shortest connection networks and some generalizations , 1957 .

[16]  Marek Gutowski.  L\'evy flights as an underlying mechanism for global optimization algorithms , 2001 .

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

[18]  David P. Dobkin,et al.  Primitives for the manipulation of three-dimensional subdivisions , 1987, SCG '87.

[19]  Franz Aurenhammer,et al.  Handbook of Computational Geometry , 2000 .

[20]  Gwendal Simon,et al.  Toward a peer-to-peer shared virtual reality , 2002, Proceedings 22nd International Conference on Distributed Computing Systems Workshops.

[21]  H. M. Gupta,et al.  The gradually truncated Levy flight for systems with power-law distributions , 1999 .

[22]  Robin Sibson,et al.  Computing Dirichlet Tessellations in the Plane , 1978, Comput. J..

[23]  Honghui Lu,et al.  Peer-to-peer support for massively multiplayer games , 2004, IEEE INFOCOM 2004.

[24]  Georges Voronoi.  Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier mémoire. Sur quelques propriétés des formes quadratiques positives parfaites. , 1908 .

[25]  Edith Cohen,et al.  Search and replication in unstructured peer-to-peer networks , 2002, ICS '02.

[27]  James M. Calvin,et al.  The SIMNET virtual world architecture , 1993, Proceedings of IEEE Virtual Reality Annual International Symposium.

[28]  Steven Fortune,et al.  Numerical stability of algorithms for 2D Delaunay triangulations , 1992, SCG '92.

[29]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[30]  Shun-Yun Hu,et al.  Scalable peer-to-peer networked virtual environment , 2004, NetGames '04.

[31]  Olivier Devillers,et al.  Perturbations and vertex removal in a 3D delaunay triangulation , 2003, SODA '03.

[32]  Stephen John Turner,et al.  Time-space consistency in large-scale distributed virtual environments , 2004, TOMC.

[33]  Jörg Liebeherr,et al.  Application-layer multicasting with Delaunay triangulation overlays , 2002, IEEE J. Sel. Areas Commun..

[34]  Hector Garcia-Molina,et al.  Designing a super-peer network , 2003, Proceedings 19th International Conference on Data Engineering (Cat. No.03CH37405).

[35]  Stefan Saroiu,et al.  A Measurement Study of Peer-to-Peer File Sharing Systems , 2001 .

[36]  C. Gold,et al.  Delete and insert operations in Voronoi/Delaunay methods and applications , 2003 .

[37]  G. Marsaglia.  Choosing a Point from the Surface of a Sphere , 1972 .

[38]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[39]  Leonidas J. Guibas,et al.  An empirical comparison of techniques for updating Delaunay triangulations , 2004, SCG '04.

[40]  James F. Doyle,et al.  Peer-to-Peer: harnessing the power of disruptive technologies , 2001, UBIQ.

[41]  Mariette Yvinec,et al.  Triangulations in CGAL , 2002, Comput. Geom..

[42]  Gwendal Simon.  Conception et réalisation d'un système pour environnement virtuel massivement partagé , 2004 .