Showing papers by "Yishay Mansour published in 1990"

The computational complexity of universal hashing

Abstract: Any implementation of Carter-Wegman universal hashing from n-bit strings to m-bit strings requires a time-space tradeoff of TS=Ω(nm) . The bound holds in the general boolean branching program model and, thus, in essentially any model of computation. As a corollary, computing a + b ∗ c in any field F requires a quadratic time-space tradeoff, and the bound holds for any representation of the elements of the field. Other lower bounds on the complexity of any implementation of universal hashing are given as well: quadratic AT2 bound for VLSI implementation; Ω( log n) parallel time bound on a CREW PRAM; and exponential size for constant-depth circuits.

The computational complexity of universal hashing

Abstract: Summary form only given. Any implementation of Carter-Wegman universal hashing from n-b strings to m-b strings requires a time-space tradeoff of TS= Omega (nm). The bound holds in the general Boolean branching program model, and thus in essentially any model of computation. As a corollary, computing a+b*c in any field F requires a quadratic time-space tradeoff, and the bound holds for any representation of the elements of the field. Other lower bounds on the complexity of any implementation of universal hashing are given as well: quadratic AT/sup 2/ bound for VLSI implementation; Omega (log n) parallel time bound on a CREW PRAM; and exponential size for constant depth circuits. The results on VLSI implementation are proved using information transfer bounds derived from the definition of a universal family of hash functions. >

Greedy packet scheduling

Abstract: Scheduling packets to be forwarded over a link is an important subtask of the routing process both in parallel computing and in communication networks This paper investigates the simple class of greedy scheduling algorithms, namely, algorithms that always forward a packet if they can It is first proved that for various “natural” classes of routes, the time required to complete the transmission of a set of packets is bounded by the sum of the number of packets and the maximal route length, for any greedy algorithm (including the arbitrary scheduling policy) Next, tight time bounds of Θ(n) are proved for a specific greedy algorithm on the class of shortest paths in n-vertex networks Finally it is shown that when the routes are arbitrary, the time achieved by various “natural” greedy algorithms can be as bad as Ω(n15), when O(n) packets have to be forwarded on an n-vertex network