Chandra Chekuri

Incremental Clustering and Dynamic Information Retrieval

Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retrieval application, and which should also be useful in other applications. The goal is to efficiently maintain clusters of small diameter as new points are inserted. We analyze several natural greedy algorithms and demonstrate that they perform poorly. We propose new deterministic and randomized incremental clustering algorithms which have a provably good performance, and which we believe should also perform well in practice. We complement our positive results with lower bounds on the performance of incremental algorithms. Finally, we consider the dual clustering problem where the clusters are of fixed diameter, and the goal is to minimize the number of clusters.

Conjunctive query containment revisited

We consider the problems of conjunctive query containment and minimization, which are known to be NP-complete, and show that these problems can be solved in polynomial time for the class of acyclic queries. We then generalize the notion of acyclicity and define a parameter called query width that captures the “degree of cyclicity” of a query: in particular, a query is acyclic if and only if its query width is 1. We give algorithms for containment and minimization that run in time polynomial in nk, where n is the input size and k is the query width. These algorithms naturally generalize those for acyclic queries, and are of practical significance because many queries have small query width compared to their sizes. We show that we can obtain good bounds on the query width of Q using the treewidth of the incidence graph of Q. Finally, we apply our containment algorithm to the practically important problem of finding equivalent rewritings of a query using a set of materialized views.

Maximizing a Monotone Submodular Function Subject to a Matroid Constraint

An improved coating pan apparatus and spray arm assembly are disclosed for providing facilitated maintenance and cleaning of sensitive spray nozzles. The spray arm assembly includes means for varying the spray length and spray angle from a position external to the coating drum. Additionally, this invention provides adjustment means for removing the fixture containing the spray nozzles entirely from the coating drum and laterally from the coating apparatus housing for purging.

Approximation schemes for minimizing average weighted completion time with release dates

We consider the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time. We present the first known polynomial time approximation schemes for several variants of this problem. Our results include PTASs for the case of identical parallel machines and a constant number of unrelated machines with and without preemption allowed. Our schemes are efficient: for all variants the running time for /spl alpha/(1+/spl epsiv/) approximation is of the form f(1//spl epsiv/, m)poly(n).

A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem

The multiple knapsack problem (MKP) is a natural and well-known generalization of the single knapsack problem and is defined as follows. We are given a set of

A recursive greedy algorithm for walks in directed graphs

n

Maximum Coverage Problem with Group Budget Constraints and Applications

items and

On Multidimensional Packing Problems

m

Approximation Algorithms for the Unsplittable Flow Problem

bins (knapsacks) such that each item

Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)

i