Vector greedy algorithms

Greedy Algorithms

Greedy vector quantization

We investigate the greedy version of the L-optimal vector quantization problem for an Rvalued random vector X ∈ L. We show the existence of a sequence (aN )N≥1 such that aN minimizes a 7→ ∥min1≤i≤N−1 |X−ai| ∧ |X−a| ∥∥ Lp (L-mean quantization error at level N induced by (a1, . . . , aN−1, a)). We show that this sequence produces L -rate optimal N -tuples a = (a1, . . . , aN ) (i.e. the L -mean q...

Greedy Algorithms: Huffman Coding

Greedy Algorithms: In an optimization problem, we are given an input and asked to compute a structure, subject to various constraints, in a manner that either minimizes cost or maximizes profit. Such problems arise in many applications of science and engineering. Given an optimization problem, we are often faced with the question of whether the problem can be solved efficiently (as opposed to a...

Parallelism and Greedy Algorithms

A number of greedy algorithms are examined <and are shown to be probably inherently sequential. Greedy algorithms are presented for finding a maximal path, for finding a . maximal set of disjoint paths in a layered dag, and for finding the largest induced subgraph of a graph that has all vertices of degree at least Ic. It is shown that for all of these algorithms, the problem of determining if ...

Distributed Greedy Pursuit Algorithms

For compressed sensing over arbitrarily connected networks, we consider the problem of estimating underlying sparse signals in a distributed manner. We introduce a new signal model that helps to describe inter-signal correlation among connected nodes. Based on this signal model along with a brief survey of existing greedy algorithms, we develop distributed greedy algorithms with low communicati...