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FOCS
2006
IEEE
14 years 2 months ago
The Effectiveness of Lloyd-Type Methods for the k-Means Problem
We investigate variants of Lloyd’s heuristic for clustering high dimensional data in an attempt to explain its popular
Rafail Ostrovsky, Yuval Rabani, Leonard J. Schulma...
FOCS
2006
IEEE
14 years 2 months ago
Input-Indistinguishable Computation
We put forward a first definition of general secure computation that, without any trusted set-up, • handles an arbitrary number of concurrent executions; and • is implementa...
Silvio Micali, Rafael Pass, Alon Rosen
FOCS
2006
IEEE
14 years 2 months ago
On the time complexity of 2-tag systems and small universal Turing machines
We show that 2-tag systems efficiently simulate Turing machines. As a corollary we find that the small universal Turing machines of Rogozhin, Minsky and others simulate Turing ma...
Damien Woods, Turlough Neary
FOCS
2006
IEEE
14 years 2 months ago
Lp metrics on the Heisenberg group and the Goemans-Linial conjecture
We prove that the function d : R3 × R3 → [0, ∞) given by d (x, y, z), (t, u, v) = (t − x)2 + (u − y)2 2 + (v − z + 2xu − 2yt)2 1 2 + (t − x)2 + (u − y)2 1 2 . is ...
James R. Lee, Assaf Naor
FOCS
2006
IEEE
14 years 2 months ago
Heat Flow and a Faster Algorithm to Compute the Surface Area of a Convex Body
We draw on the observation that the amount of heat diffusing outside of a heated body in a short period of time is proportional to its surface area, to design a simple algorithm f...
Mikhail Belkin, Hariharan Narayanan, Partha Niyogi