Jeanette P. Schmidt

Chernoff-Hoeffding Bounds for Applications with Limited Independence

Chernoff-Hoeffding (CH) bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables (r.v.s). We present a simple technique that gives slightly better bounds than these and that more importantly requires only limited independence among the random variables, thereby importing a variety of standard results to the case of limited independence for free. Additional methods are also presented, and the aggregate results are sharp and provide a better understanding of the proof techniques behind these bounds. These results also yield improved bounds for various tail probability distributions and enable improved approximation algorithms for jobshop scheduling. The limited independence result implies that a reduced amount and weaker sources of randomness are sufficient for randomized algorithms whose analyses use the CH bounds, e.g., the analysis of randomized algorithms for random sampling and oblivious packet routing.

All Highest Scoring Paths in Weighted Grid Graphs and Their Application to Finding All Approximate Repeats in Strings

Weighted paths in directed grid graphs of dimension (m X n) can be used to model the string edit problem, which consists of obtaining optimal (weighted) alignments between substrings of A, |A|=m, and substrings of B, |B|=n. We build a data structure (in O(mn log m) time) that supports O(log m) time queries about the weight of any of the O(m2n) best paths from the vertices in column 0 of the graph to all other vertices. Using these techniques we present a simple O(n2 log n) time and

Load-sharing in heterogeneous systems via weighted factoring

\Theta(n^2)

The spatial complexity of oblivious k -probe Hash functions

space algorithm to find all (the locally optimal) approximate tandem (or nontandem) repeats xy within a string of size n. This improves (by a factor of log n) upon several previous algorithms for this problem and is the first algorithm to find all locally optimal repeats. For edit graphs with weights in {0, -1, 1}, a slight modification of our techniques yields an O(n2) algorithm for the cyclic string comparison problem, as compared to O(n2 log n) for the case of general weights.

An Algorithm for Approximate Tandem Repeats

Jeanette Schmidt~ R. N. Uma

Identifying periodic occurrences of a template with applications to protein structure

Joel Wein~ We consider the problem of scheduling a parallel loop with independent iterations on a network of heterogeneous workstations, and demonstrate the effectiveness of a variant of fa.toring, a scheduling policy originating in the context of shared address-space homogeneous multiprocessors. In the new scheme, weighted factoring, processors are dynamically assigned decreasing size chunks of iterations in proportion to their processing speeds. Through experiments on a network of SUN Spare workstations we show that weighted factoring significantly outperforms variants of a work-stea!ing load-balancing algorithm and on certain applications dramatically outperforms factoring as well. We then study weighted work assignment analytically, giving upper and lower bounds on its performance under the assumption that the processor iteration execution times can be modeled as weighted random variables. *Department of Computer Science,Polytechmc Umverslty, Brooklyn, NY, 11201. Researchsupported by ARPA/USAF under Grant no F30602-95-1-OO08and the New York State Science and Technology Foundation through Its center for Advanced Technology in Telecommunications Joel Wein wassupported in part by NSF Grant CCR-9211494, and Jeanette Schmidt m part by NSF grant CCR9305873. thummelQmono poly edu (Contact Author) *JpsC!qmcs4 poly.edu

On the Dynamic Finger Conjecture for Splay Trees. Part I: Splay Sorting log n -Block Sequences

ruma@photon.poly .edu ~ wein@mem poly. edu. Permissionto makedigitallhard copiesof all or pastof thk material for personalor classroomuseis grantedwithout fee provided that the copies are not madeor dktributed for profit or commercialadvantage,the copyright notice, the title of the publication and its dateappear,and notice is given that copyright is by permissionof the ACM, Inc. To copy otherwise, to republish, to post on serversor to redistributeto lists, requiresspecific riersnissionand/or fee.

The analysis of closed hashing under limited randomness

The problem of constructing a dense static hash-based lookup table T for a set of n elements belonging to a universe

Nonoblivious hashing

U = \{ 0, 1, 2,\cdots , m -1 \}

Non-oblivious hashing

is considered. Nearly tight bounds on the spatial complexity of oblivious