Motivated by applications to sensor networks and privacy preserving databases, we consider the problem of functional compression. The objective is to separately compress possibly correlated discrete sources such that an arbitrary but fixed deterministic function of those sources can be computed given the compressed data from each source. We consider both the lossless and lossy computation of a function. Specifically, we present results of the rate regions for three instances of the problem where there are two sources: 1) lossless computation where one source is available at the decoder; 2) under a special condition, lossless computation where both sources are separately encoded; and 3) lossy computation where one source is available at the decoder. For all of these instances, we present a layered architecture for distributed coding: first preprocess data at each source using colorings of certain characteristic graphs and then use standard distributed source coding (a laSlepian and Wolfs scheme) to compress them. For the first instance, our results extend the approach developed by Orlitsky and Roche (2001) in the sense that our scheme requires simpler structure of coloring rather than independent sets as in the previous case. As an intermediate step to obtain these results, we obtain an asymptotic characterization of conditional graph coloring for an OR product of graphs generalizing a result of Korner (1973), which should be of interest in its own right.

In this paper, we consider the problem of designing a scheduling algorithm for input queued switches, that is both fair as well as throughput optimal. Most of the existing literature on input-queued switch fairness criteria concentrates on flow-based fairness. Since a large fraction of network traffic is about "short- flows" there is a need for packet-based fairness criterion. The significant body of literature developed over the past two decades for packet-based scheduling algorithms is primarily concerned with throughput and delay, but not fairness. One of the reasons for such a state of affairs is the lack of a proper definition for packet-based fairness. The difficulty in defining fair stems from the fact that any reasonable notion of fairness must combine the well-known notion of fairness for a single-queue with the scheduling constraint of an input queued switch in an appropriate manner. As one of the main results of this paper, we define a notion of packet-based fair scheduling by identifying it as the selection of a winner in the following ranked election: packets are voters; schedules are candidates and each packet ranks different schedules based on their priorities. Drawing upon the seminal work of Goodman and Markowitz (1952) on ranked elections, we obtain a unique characterization of the fair schedule. Another important contribution of this paper is proving that the thus obtained fair scheduling algorithm is throughput optimal. There is no a priori reason why this should be true, and we introduce some non-standard proof techniques to prove the result. Our results suggest a framework for defining fair scheduling algorithm for a constrained packet network; a nonstandard method to prove throughput stability for algorithms, such as ours, that are not based on queue-sizes.

We consider the distributed computation of a function of random sources with minimal communication. Specifically, given two discrete memoryless sources, X and Y, a receiver wishes to compute f(X, Y) based on (encoded) information sent from X and Y in a distributed manner. A special case, f(X, Y) = (X, Y), is the classical question of distributed source coding considered by Slepian and Wolf (1973). Orlitsky and Roche (2001) considered a somewhat restricted setup when Y is available as side information at the receiver. They characterized the minimal rate at which X needs to transmit data to the receiver as the conditional graph entropy of the characteristic graph of X based on f. In our recent work (2006), we further established that this minimal rate can be achieved by means of graph coloring and distributed source coding (e.g. Slepian-Wolf coding). This characterization allows for the separation between "function coding" and "correlation coding." In this paper, we consider a more general setup where X and Y are both encoded (separately). This is a significantly harder setup for which to give a single-letter characterization for the complete rate region. We find that under a certain condition on the support set of X and Y (called the zigzag condition), it is possible to characterize the rate region based on graph colorings at X and Y separately. That is, any achievable pair of rates can be realized by means of first coloring graphs at X and Y separately (function coding) and then using Slepian-Wolf coding for these colors (correlation coding). We also obtain a single-letter characterization of the minimal joint rate. Finally, we provide simulation results based on graph coloring to establish the rate gains on real sequences

We consider the following rate distortion problem: given a source X and correlated, decoder side information Y, find the minimum encoding rate for X required to compute f(X,Y) at the decoder within distortion D. This is a generalization of the classical Wyner-Ziv setup and was resolved by Yamamoto (1982). However, this result involved an auxiliary random variable that lacks explicit meaning. To provide a more direct link between this variable and the function f, Orlitsky and Roche (2001) established the minimal rate required in the zero-distortion case as an extension of Korner's graph entropy. Recently, we (with Jaggi) showed that the zero-distortion rate can be achieved by minimum entropy graph coloring of an appropriate product graph. This leads to a modular architecture for functional source coding with a preprocessing "functional coding" scheme operating on top of a classical Slepian-Wolf source coding scheme. In this paper, we give a characterization of Yamamoto's rate distortion function in terms of a reconstruction function. This (non-single-letter) characterization is an extension of our previous results as well as Orlitsky and Roche's results. We obtain a modular scheme operating with Slepian-Wolf's scheme for the problem of functional rate distortion. Further, we give an achievable rate (with single-letter characterization) utilizing this scheme that intuitively extends our previous results.

Swoogle is a crawler-based indexing and retrieval system for the Semantic Web. It extracts metadata for each discovered document, and computes relations between documents. Discovered documents are also indexed by an information retrieval system which can use either character N-Gram or URIrefs as keywords to find relevant documents and to compute the similarity among a set of documents. One of the interesting properties we compute is ontology rank, a measure of the importance of a Semantic Web document.