Abstract — This paper describes Scalable Reliable Multicast (SRM), a reliable multicast framework for light-weight sessions and application level framing. The algorithms of this framework are efficient, robust, and scale well to both very large networks and very large sessions. The SRM framework has been prototyped in wb, a distributed whiteboard application, which has been used on a global scale with sessions ranging from a few to a few hundred participants. The paper describes the principles that have guided the SRM design, including the IP multicast group delivery model, an end-to-end, receiver-based model of reliability, and the application level framing protocol model. As with unicast communications, the performance of a reliable multicast delivery algorithm depends on the underlying topology and operational environment. We investigate that dependence via analysis and simulation, and demonstrate an adaptive algorithm that uses the results of previous loss recovery events to adapt the control parameters used for future loss recovery. With the adaptive algorithm, our reliable multicast delivery algorithm provides good performance over a wide range of underlying topologies. Index Terms—Computer networks, computer network performance, Internetworking.

The distribution of hard graph coloring problems as a function of graph connectivity is shown to have two distinct transition behaviors. The first, previously recognized, is a peak in the median search cost near the connectivity at which half the graphs have solutions. This region contains a high proportion of relatively hard problem instances. However, the hardest instances are in fact concentrated at a second, lower, transition point. Near this point, most problems are quite easy, but there are also a few very hard cases. This region of exceptionally hard problems corresponds to the transition between polynomial and exponential scaling of the average search cost, whose location we also estimate theoretically. These behaviors also appear to arise in other constraint problems. This work also shows the limitations of simple measures of the cost distribution, such as mean or median, for identifying outlying cases. 1

4, and Toby Walsh 5

where these ideas were initially discussed and much of the work was done. We are especially grateful to John Padgett, organizer of the States and Markets group at SFI for his support and insights. We have benefited from comments from the audience at seminars

We prove a new switching lemma that works for restrictions that set only a small fraction of the variables and is applicable to DNFs with small conjunctions. We use this to prove lower bounds for the Res(k) propositional proof system, an extension of resolution which works with k-DNFs instead of clauses. We also obtain an exponential separation between depth d circuits of k + 1.

We present a new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the so-called replicator equations—a class of straightforward continuous- and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate mean-field annealing heuristics.

X and Y are random variables. Person PX knows X, Person P Y knows Y , and both know the joint probability distribution of the pair (X; Y ). Using a predetermined protocol, they communicate over a binary, error-free, channel in order for P Y to learn X. PX may or may not learn Y . How many information bits must be transmitted (by both persons) in the worst case if only m messages are allowed? C 1 (XjY ) is the number of bits required when at most one message is allowed, necessarily from PX to P Y . C 2 (XjY ) is the number of bits required when at most two messages are permitted: P Y transmits a message to PX , then PX responds with a message to P Y . C1 (XjY ) is the number of bits required when communication is unrestricted: PX and P Y can communicate back and forth. The maximum reduction in communication achievable via interaction is almost logarithmic. For all (X; Y ) pairs, C1 (XjY ) dlog C 1 (XjY )e + 1, whereas, for a class of (X; Y ) pairs, C1 (XjY ) = dlog C 1 (...

We dene the `frozen development' of coloring random graphs. We identify two nodes in a graph as frozen if they are the same color in all legal colorings. This is analogous to studies of the development of a backbone or spine in SAT (the Satisability problem). We rst describe in detail the algorithmic techniques used to study frozen development. We present strong empirical evidence that freezing in 3-coloring is sudden. A single edge typically causes the size of the graph to collapse in size by 28%. We also use the frozen development to calculate unbiased estimates of probability of colorability in random graphs, even where this probability is as low as 10 300 . We investigate the links between frozen development and the solution cost of graph coloring. In SAT, a discontinuity in the order parameter has been correlated with the hardness of SAT instances, and our data for coloring is suggestive of an asymptotic discontinuity. The uncolorability threshold is known to give rise to har...

Our study in this paper focuses on implementing parallel spanning tree algorithms on SMPs. Spanning tree is an important problem in the sense that it is the building block for many other parallel graph algorithms and also because it is representative of a large class of irregular combinatorial problems that have simple and efficient sequential implementations and fast PRAM algorithms, but often have no known efficient parallel implementations. In this paper we present a new randomized algorithm and implementation with superior performance that for the first-time achieves parallel speedup on arbitrary graphs (both regular and irregular topologies) when compared with the best sequential implementation for finding a spanning tree. This new algorithm uses several techniques to give an expected running time that scales linearly with the number p of processors for suitably large inputs (n> p 2). As the spanning tree problem is notoriously hard for any parallel implementation to achieve reasonable speedup, our study may shed new light on implementing PRAM algorithms for shared-memory parallel computers. The main results of this paper are 1. A new and practical spanning tree algorithm for symmetric multiprocessors that exhibits parallel speedups on graphs with regular and irregular topologies; and 2. An experimental study of parallel spanning tree algorithms that reveals the superior performance of our new approach compared with the previous algorithms. The source code for these algorithms is freely-available from our web site hpc.ece.unm.edu.

Rapid access to information is essential for a wide variety of retrieval systems and applications. Hashing has long been used when the fastest possible direct search is desired, but is generally not appropriate when sequential or range searches are also required. This paper describes a hashing method, developed for collections that are relatively static, that supports both direct and sequential access. Indeed, the algorithm described gives hash functions that are optimal in terms of time and hash table space utilization, and that preserve any a priori ordering desired. Furthermore, the resulting order preserving minimal perfect hash functions (OPMPHFs) can be