Sanjeev Khanna

Space-efficient online computation of quantile summaries

An ∈-approximate quantile summary of a sequence of N elements is a data structure that can answer quantile queries about the sequence to within a precision of ∈N. We present a new online algorithm for computing∈-approximate quantile summaries of very large data sequences. The algorithm has a worst-case space requirement of &Ogr;(1÷∈ log(∈N)). This improves upon the previous best result of &Ogr;(1÷∈ log2(∈N)). Moreover, in contrast to earlier deterministic algorithms, our algorithm does not require a priori knowledge of the length of the input sequence. Finally, the actual space bounds obtained on experimental data are significantly better than the worst case guarantees of our algorithm as well as the observed space requirements of earlier algorithms.

Complexity classifications of boolean constraint satisfaction problems

Preface 1. Introduction 2. Complexity Classes 3. Boolean Constraint Satisfaction Problems 4. Characterizations of Constraint Functions 5. Implementation of Functions and Reductions 6. Classification Theorems for Decision, Counting and Quantified Problems 7. Classification Theorems for Optimization Problems 8. Input-Restricted Constrained Satisfaction Problems 9. The Complexity of the Meta-Problems 10. Concluding Remarks Bibliography Index.

Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems

We study the approximability of edge-disjoint paths and related problems. In the edge-disjoint paths problem (EDP), we are given a network G with source-sink pairs (si; ti), 1 i k, and the goal is to nd a largest subset of source-sink pairs that can be simultaneously connected in an edge-disjoint manner. We show that in directed networks, for any > 0, EDP is NP-hard to approximate within m 1=2 . We also design simple approximation algorithms that achieve essentially matching approximation guarantees for some generalizations of EDP. Another related class of routing problems that we study concerns EDP with the additional constraint that the routing paths be of bounded length. We show that, for any > 0, bounded length EDP is hard to approximate within m 1=2 even in undirected networks, and give an O( p m)-approximation algorithm for it. For directed networks, we show that even the single source-sink pair case (i.e. nd the maximum number of paths of bounded length between a given sourcesink pair) is hard to approximate within m 1=2 , for any > 0.

On propagation of deletions and annotations through views

We study two classes of view update problems in relational databases. We are given a source database S, a monotone query Q, and the view Q(S) generated by the query. The first problem that we consider is the classical view deletion problem where we wish to identify a minimal set T of tuples in S whose deletion will eliminate a given tuple t from the view. We study the complexity of optimizing two natural objectives in this setting, namely, find T to minimize the side-effects on the view, and the source, respectively. For both objective functions, we show a dichotomy in the complexity. Interestingly, the problem is either in P or is NP-hard, for queries in the same class in either objective function.The second problem in our study is the annotation placement problem. Suppose we annotate an attribute of a tuple in S. The rules for carrying the annotation forward through a query are easily stated. On the other hand, suppose we annotate an attribute of a tuple in the view Q(S), what annotation(s) in S will cause this annotation to appear in the view, minimizing the propagation to other attributes in Q(S)? View annotation is becoming an increasingly useful method of communicating meta-data among users of shared scientific data sets, and to our knowledge, there has been no formal study of this problem.Our study of these problems gives us important insights into computational issues involved in data provenance or lineage --- the process by which data moves through databases. We show that the two problems correspond to two fundamentally distinct notions of provenance, why and where-provenance.

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

Power-conserving computation of order-statistics over sensor networks

n

On the hardness of approximating the chromatic number

items and

On Multidimensional Packing Problems

m

Archiving scientific data

bins (knapsacks) such that each item