Koorde is a new distributed hash table (DHT) based on Chord [15] and the de Bruijn graphs [2]. While inheriting the simplicity of Chord, Koorde meets various lower bounds, such as O(log n) hops per lookup request with only 2 neighbors per node (where n is the number of nodes in the DHT), and O(log n/ log log n) hops per lookup request with O(log n) neighbors per node.

Contents 1 Introduction 5 1.1 Computer Chess and Artificial Intelligence : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.2 History of Computer Chess : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.3 Results : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 1.4 Overview : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 1.5 Basic Definitions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 2 The Sequential Game Tree Search Algorithm 13 2.1 The Scout-Algorithm : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13 2.2 fffi-Enhancements : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 21 2.2.1 Transposition Table<F7.77

Routing topologies for distributed hashing in peer-to-peer networks are classified into two categories: deterministic and randomized. A general technique for constructing determin-istic routing topologies is presented. Using this technique, classical parallel interconnection networks can be adapted to handle the dynamic nature of participants in peer-to-peer networks. A unified picture of randomized routing topolo-gies is also presented. Two new protocols are described which improve average latency as a function of out-degree. One of the protocols can be shown to be optimal with high probability. Finally, routing networks for distributed hash-ing are revisited from a systems perspective and several open design problems are listed.

Custom-designed DNA arrays offer the possibility of simultaneously monitoring thousands of hybridization reactions These arrays show great potential for many medical and scientific applications such as polymorphism analysis and genotyping. Relatively high costs are associated with the need to specifically design and synthesize problem specific arrays. Recently, an alternative approach was suggested that utilizes fixed, universal arrays. This approach presents an interesting design problem--the arrays should contain as many probes as possible, while minimizing experimental error ~ caused by cross-hybridization. We use a simple thermodynamic model to cast this design problem in a formal mathematical framework. Employing new combinatorial ideas, we derive an efficient construction for the design problem, and prove that our construction is near-optimal. 1

this paper, we consider a variety of problems with application to sequencing by hybridization. First, we develop a theory of interactive sequencing by hybridization, based on

Peer-to-peer (P2P) systems are typically divided into those that centralize lookup functionality in a single location and those that distribute the lookup operation across the set of participating hosts. The former approach can offer constant time lookup latency, but is more expensive to scale and suffers from single points of failure. In contrast, the fully distributed approach is easier to scale and can be more resilient to failures, but the lookup latency scales as a function of the total number of participants. While the research community has made great progress in improving the latency of distributed lookup, these systems, exemplified by Chord[17], typically require O(logN) hops to locate an object in a system with N hosts. In this paper, we explore the costs and benefits of a new hybrid approach that partially distributes lookup information among a dynamically adjusted set of high-capacity "superpeers". This design exploits the resource heterogeneity inherent in existing P2P systems to provide many of the advantages of a centralized system, even while avoiding most of the problems associated with such systems. Lookup is performed using superpeers in constant-time, and the system performs well even in the event of simultaneous superpeer failures. Finally, while our gain in performance is potentially at the expense of scalability, we will show that a straightforward implementation should be able to scale to over one million peers with reasonable lookup rates.

We show how to implement the fffi-enhancements like iterative deepening, transposition tables, history tables etc. used in sequential chess programs in a distributed system such that the distributed algorithm profits by these heuristics as well as the sequential does. Moreover the methods we describe are suitable for very large distributed systems. We implemented these fffi-enhancements in the distributed chess program ZUGZWANG. For a distributed system of 64 processors we obtain a speedup between 28 and 34 running at tournament speed. The basis for this chess program is a distributed fffi-algorithm with very good load balancing properties combined with the use of a distributed transposition table that grows with the size of the distributed system. 1. INTRODUCTION In this paper we describe a fully distributed chess program ZUGZWANG running on a network of Transputers. We present experimental results that show the efficiency of our implementation. The good behavior of the sequential f...

Abstract not found

A (k n ; n) k -de Bruijn Cycle is a cyclic k-ary sequence with the property that every k-ary n-tuple appears exactly once contiguously on the cycle. A (k r ; k s ; m; n) k -de Bruijn Torus is a k-ary k r k s toroidal array with the property that every k-ary m n matrix appears exactly once contiguously on the torus. As is the case with de Bruijn cycles, the 2-dimensional version has many interesting applications, from coding and communications to pseudo-random arrays, spectral imaging, and robot self-location. J.C. Cock proved the existence of such tori for all m; n; and k, and Chung, Diaconis, and Graham asked if it were possible that r = s and m = n for n even. Fan, Fan, Ma and Siu showed this was possible for k = 2. Combining new techniques with old, we prove the result for k 2 and show that actually much more is possible. The cases in 3 or more dimensions remain.

A thrackle is a graph drawn in the plane so that its edges are represented by Jordan arcs and any two distinct arcs either meet at exactly one common vertex or cross at exactly one point interior to both arcs. About forty years ago, J. H. Conway conjectured that the number of edges of a thrackle cannot exceed the number of its vertices. We show that a thrackle has at most twice as many edges as vertices. Some related problems and generalizations are also considered. 1