A General Theory of Semi-Unification

Various restrictions on the terms allowed for substitution give rise to different cases of semi-unification. Semi-unification on finite and regular terms has already been considered in the literature. We introduce a general case of semi-unification where substitutions are allowed on non-regular terms, and we prove the equivalence of this general case to a well-known undecidable data base dependency problem, thus establishing the undecidability of general semi-unification. We present a unified way of looking at the various problems of semi-unification. We give some properties that are common to all the cases of semi-unification. We also the principality property and the solution set for those problems. We prove that semi-unification on general terms has the principality property. Finally, we present a recursive inseparability result between semi-unification on regular terms and semi-unification on general terms.

Cluster-Based Optimizations for Distributed Hash Tables

We consider the problem of performing topological optimizations of distributed hash tables. Such hash tables include Chord and Tapestry and are a popular building block for distributed applications. Optimizing topologies over one dimensional hash spaces is particularly difficult as the higher dimensionality of the underlying network makes close fits unlikely. Instead, current schemes are limited to heuristically performing local optimizations finding the best of small random set of peers. We propose a new class of topology optimizations based on the existence of clusters of close overlay members within the underlying network. By constructing additional overlays for each cluster, a significant portion of the search procedure can be performed within the local cluster with a corresponding reduction in the search time. Finally, we discuss the effects of these additional overlays on spatial locality and other load balancing scheme.

Load Balancing a Cluster of Web Servers using Distributed Packet Rewriting

In this paper, we propose and evaluate an implementation of a prototype scalable web server. The prototype consists of a load-balanced cluster of hosts that collectively accept and service TCP connections. The host IP addresses are advertised using the Round Robin DNS technique, allowing any host to receive requests from any client. Once a client attempts to establish a TCP connection with one of the hosts, a decision is made as to whether or not the connection should be redirected to a different host---namely, the host with the lowest number of established connections. We use the low-overhead Distributed Packet Rewriting (DPR) technique to redirect TCP connections. In our prototype, each host keeps information about connections in hash tables and linked lists. Every time a packet arrives, it is examined to see if it has to be redirected or not. Load information is maintained using periodic broadcasts amongst the cluster hosts.