Alan Siegel

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.

The spatial complexity of oblivious k -probe Hash functions

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

On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications

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

On Universal Classes of Extremely Random Constant-Time Hash Functions

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

Optimal wiring between rectangles

O(1)

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

-probe hash functions, which are defined to depend solely on their search key argument, are provided. This establishes a significant gap between oblivious and nonoblivious search. In particular, the results include the following: • A lower bound showing that oblivious k-probe hash functions require a program size of

The Separation for General Single-Layer Wiring Barriers

\Omega(({n / k}^{2})e^{-k}+\log \log m)

The analysis of closed hashing under limited randomness

bits, on average. • A probabilistic construction of a family of oblivious k-probe hash functions that can be specified in

Nonoblivious hashing

O(n e^{-k} +\log \log m)

Non-oblivious hashing

bits, which nearly matches the above lower bound. • A variation of an explicit