15 research outputs found
An approximation algorithm for #k-SAT
"Vegeu el resum a l'inici del document del fitxer adjunt"
An Approximation Algorithm for #k-SAT
We present a simple randomized algorithm that approximates the number of
satisfying assignments of Boolean formulas in conjunctive normal form. To the
best of our knowledge this is the first algorithm which approximates #k-SAT for
any k >= 3 within a running time that is not only non-trivial, but also
significantly better than that of the currently fastest exact algorithms for
the problem. More precisely, our algorithm is a randomized approximation scheme
whose running time depends polynomially on the error tolerance and is mildly
exponential in the number n of variables of the input formula. For example,
even stipulating sub-exponentially small error tolerance, the number of
solutions to 3-CNF input formulas can be approximated in time O(1.5366^n). For
4-CNF input the bound increases to O(1.6155^n).
We further show how to obtain upper and lower bounds on the number of
solutions to a CNF formula in a controllable way. Relaxing the requirements on
the quality of the approximation, on k-CNF input we obtain significantly
reduced running times in comparison to the above bounds
A Casual Tour Around a Circuit Complexity Bound
I will discuss the recent proof that the complexity class NEXP
(nondeterministic exponential time) lacks nonuniform ACC circuits of polynomial
size. The proof will be described from the perspective of someone trying to
discover it.Comment: 21 pages, 2 figures. An earlier version appeared in SIGACT News,
September 201
Modern Lower Bound Techniques in Database Theory and Constraint Satisfaction
Conditional lower bounds based on , the Exponential-Time Hypothesis (ETH), or similar complexity assumptions can provide very useful information about what type of algorithms are likely to be possible. Ideally, such lower bounds would be able to demonstrate that the best known algorithms are essentially optimal and cannot be improved further. In this tutorial, we overview different types of lower bounds, and see how they can be applied to problems in database theory and constraint satisfaction
On optimality of exact and approximation algorithms for scheduling problems
We consider the classical scheduling problem on parallel identical machines to minimize the makespan. Under the exponential time hypothesis (ETH), lower bounds on the running times of exact and approximation algorithms are characterized