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Peeling Arguments and Double Hashing
| Citations: | 2 - 1 self |
BibTeX
@MISC{Mitzenmacher_peelingarguments,
author = {Michael Mitzenmacher and Justin Thaler},
title = {Peeling Arguments and Double Hashing},
year = {}
}
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Abstract
The analysis of several algorithms and data structures can be reduced to the analysis of the following greedy “peeling” process: start with a random hypergraph; find a vertex of degree at most k, and remove it and all of its adjacent hyperedges from the graph; repeat until there is no suitable vertex. This specific process finds the k-core of a hypergraph, and variations on this theme have proven useful in analyzing for example decoding from low-density parity-check codes, several hash-based data structures such as cuckoo hashing, and algorithms for satisfiability of random formulae. This approach can be analyzed several ways, with two common approaches being via a corresponding branching process or a fluid limit family of differential equations. In this paper, we make note of an interesting aspect of these types of processes: the results are generally the same when the randomness is structured in the manner of double hashing. This phenomenon allows us to use less randomness and simplify the implementation for several hash-based data structures and algorithms. We explore this approach from both an empirical and theoretical perspective, examining theoretical justifications as well as simulation results for specific problems.
Keyphrases
double hashing several hash-based data structure interesting aspect data struc-tures adjacent hyperedges common approach following greedy corresponding branching process differential equation suitable vertex several way theoretical justification several algorithm theoretical perspective cuckoo hashing low-density parity-check code simulation result specific process random hypergraph fluid limit family random formula specific problem
