Robust consensus computation

Random Consensus Robust PCA

In this section we give the proof of Theorem 1. Recall that Ω is a d×(d−r) matrix, and that ωi ⊂ {1, . . . , d} indexes the r + 1 nonzero entries in the i column of Ω. Each ωi indicates the coordinates of a projection of U that we aim to identify. Since r2pca selects a matrix Ω satisfying (i), Lemma 1 implies that if we find the projections of U onto the coordinates indicated in Ω, then we can ...

Towards Robust Quantum Computation

It has been shown in the past two decades that quantum devices can achieve useful information processing tasks impossible in classical devices. Meanwhile, the development of quantum error correcting codes and fault-tolerant computation methods has also set down a solid theoretical promise to overcome decoherence. However, to-date, we have not been able to apply such quantum information processi...

Robust Network Computation

In this thesis, we present various models of distributed computation and algorithms for these models. The underlying theme is to come up with fast algorithms that can tolerate faults in the underlying network. We begin with the classical message-passing model of computation, surveying many known results. We give a new, universally optimal, edge-biconnectivity algorithm for the classical model. ...

A Robust Dna Computation

Robust Geometric Computation

Geometric algorithms are often composed of a set of basic geometric predicates and constructions, also called primitives. Correctness of an algorithm is usually proved under the assumption that all primitives return the correct result. This is in sharp contrast to the naive, but common strategy of implementing such primitives with fixed-precision floating-point arithmetic. The disastrous effect...