An Almost Optimal Algorithm for Computing Nonnegative Rank
نویسندگان
چکیده
منابع مشابه
A Singly-Exponential Time Algorithm for Computing Nonnegative Rank
Here, we give an algorithm for deciding if the nonnegative rank of a matrix M of dimension m × n is at most r which runs in time (nm)O(r2). This is the first exact algorithm that runs in time singly-exponential in r. This algorithm (and earlier algorithms) are built on methods for finding a solution to a system of polynomial inequalities (if one exists). Notably, the best algorithms for this ta...
متن کاملComputing Symmetric Nonnegative Rank Factorizations
An algorithm is described for the nonnegative rank factorization (NRF) of some completely positive (CP) matrices whose rank is equal to their CP-rank. The algorithm can compute the symmetric NRF of any nonnegative symmetric rank-r matrix that contains a diagonal principal submatrix of that rank and size with leading cost O(rm) operations in the dense case. The algorithm is based on geometric co...
متن کاملAn Almost Optimal PAC Algorithm
The best currently known general lower and upper bounds on the number of labeled examples needed for learning a concept class in the PAC framework (the realizable case) do not perfectly match: they leave a gap of order log(1/ ) (resp. a gap which is logarithmic in another one of the relevant parameters). It is an unresolved question whether there exists an “optimal PAC algorithm” which establis...
متن کاملAn Almost Optimal Algorithm for Unbounded Searching
Unbounded searching can be viewed as searching an ordered table of infinite size. In this paper we present an algorithm for unbounded searching and derive a lower bound on the number of comparisons required which shows that the algorithm is very nearly optimal. (Submitted to Information Processing Letters) * Work supported in part by U. S. Energy Research and Development Administration under co...
متن کاملAn Almost-Optimal Algorithm for the Assembly Line Scheduling Problem
This paper considers a solution to the multiprocessor scheduling problem for the case where the ordering relation between tasks can be represented as a tree. Assume that we have n identical processors, and a number of tasks to perform. Each task T i requires an amount of time pi to complete, 0 < CL. 1 i k, so that k is an upper bound on task length. Tasks are indivisible, so that a processor on...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2016
ISSN: 0097-5397,1095-7111
DOI: 10.1137/140990139