On the Complexity of Sparse Elimination

The Communication Complexity of Enumerat

The Communication Complexity of Enumeration, Elimination, and Selection

✍ Andris Ambainis; Harry Buhrman; William Gasarch; Bala Kalyanasundaram; Leen Tore 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 278 KB

Let k, n ¥ N and f: {0, 1} n × {0, 1} n Q {0, 1}. Assume Alice has x 1 , ..., x k ¥ {0, 1} n , Bob has y 1 , ..., y k ¥ {0, 1} n , and they want to compute municating as few bits as possible. The direct sum conjecture (henceforth DSC) n (log log(n))(log(n)) ) bits. This establishes a weak randomize

On the Number of Sparse RSA Exponents

✍ William D. Banks; Igor E. Shparlinski 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 109 KB

An RSA modulus is a product M ¼ pl of two primes p and l. We show that for almost all RSA moduli M, the number of sparse exponents e (which allow for fast RSA encryption) with the property that gcdðe; jðMÞÞ ¼ 1 (hence RSA decryption can also be performed) is very close to the expected value.

On the complexity of task allocation

✍ A. Schoneveld; J. F. de Ronde; P. M. A. Sloot 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 134 KB 👁 3 views

A detailed study is presented on the combinatorial optimization problem of allocating parallel tasks to a parallel computer. Depending on two application/machine-specific parameters, both a sequential and a parallel optimal allocation phase are shown to exist. A sudden "phase" transition is observed

On the Complexity of Database Queries

✍ Christos H. Papadimitriou; Mihalis Yannakakis 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 223 KB

We revisit the issue of the complexity of database queries, in the light of the recent parametric refinement of complexity theory. We show that, if the query size (or the number of variables in the query) is considered as a parameter, then the relational calculus and its fragments (conjunctive queri

On the Complexity of k-SAT

✍ Russell Impagliazzo; Ramamohan Paturi 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 114 KB

The k-SAT problem is to determine if a given k-CNF has a satisfying assignment. It is a celebrated open question as to whether it requires exponential time to solve k-SAT for k 3. Here exponential time means 2 $n for some $>0. In this paper, assuming that, for k 3, k-SAT requires exponential time co

On the Complexity of Analytic Sets

✍ Karel Hrbacek 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 463 KB 👁 1 views