• Publications
  • Influence
An Introduction to Computational Learning Theory
The probably approximately correct learning model Occam's razor the Vapnik-Chervonenkis dimension weak and strong learning learning in the presence of noise inherent unpredictability reducibility inExpand
Quantum Complexity Theory
TLDR
This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation. Expand
An optimal algorithm for on-line bipartite matching
TLDR
This work applies the general approach to data structures, bin packing, graph coloring, and graph coloring to bipartite matching and shows that a simple randomized on-line algorithm achieves the best possible performance. Expand
Quantum complexity theory
TLDR
This dissertation proves that relative to an oracle chosen uniformly at random, the class NP cannot be solved on a quantum Turing machine in time $o(2\sp{n/2}).$ and gives evidence suggesting that quantum Turing Machines cannot efficiently solve all of NP. Expand
Strengths and Weaknesses of Quantum Computing
TLDR
It is proved that relative to an oracle chosen uniformly at random with probability 1 the class $\NP$ cannot be solved on a quantum Turing machine (QTM) in time $o(2^{n/2})$. Expand
Matching is as easy as matrix inversion
TLDR
A new algorithm for finding a maximum matching in a general graph with special feature is that its only computationally non-trivial step is the inversion of a single integer matrix, the isolating lemma. Expand
Expander flows, geometric embeddings and graph partitioning
TLDR
An interesting and natural "certificate" for a graph's expansion is described, by embedding an n-node expander in it with appropriate dilation and congestion, and is called an expander flow. Expand
Quantum walks on graphs
TLDR
A lower bound on the possible speed up by quantum walks for general graphs is given, showing that quantum walks can be at most polynomially faster than their classical counterparts. Expand
AdWords and Generalized On-line Matching
TLDR
The notion of a tradeoff revealing LP is introduced and used to derive two optimal algorithms achieving competitive ratios of 1-1/e for this problem of online bipartite matching. Expand
Expander flows, geometric embeddings and graph partitioning
TLDR
An interesting and natural “approximate certificate” for a graph's expansion, which involves embedding an n-node expander in it with appropriate dilation and congestion, is described. Expand
...
1
2
3
4
5
...