217,709 research outputs found
Exact Algorithms for 0-1 Integer Programs with Linear Equality Constraints
In this paper, we show -time and -space exact
algorithms for 0-1 integer programs where constraints are linear equalities and
coefficients are arbitrary real numbers. Our algorithms are quadratically
faster than exhaustive search and almost quadratically faster than an algorithm
for an inequality version of the problem by Impagliazzo, Lovett, Paturi and
Schneider (arXiv:1401.5512), which motivated our work. Rather than improving
the time and space complexity, we advance to a simple direction as inclusion of
many NP-hard problems in terms of exact exponential algorithms. Specifically,
we extend our algorithms to linear optimization problems
Quantum Computing Algorithms for Solving Complex Mathematical Problems
The power of quantum mechanics, that is too complex for conventional computers, can be solved by an innovative model of computing known as quantum computing. Quantum algorithms can provide exponential speedups for some types of problems, such as many difficult mathematical ones. In this paper, we review some of the most important quantum algorithms for hard mathematical problems. When factoring large numbers, Shor's algorithm is orders of magnitude faster than any other known classical algorithm. The Grover's algorithm, which searches unsorted databases much more quickly than conventional algorithms, is then discussed.  
Optimal recombination in genetic algorithms for combinatorial optimization problems: Part II
This paper surveys results on complexity of the optimal recombination problem
(ORP), which consists in finding the best possible offspring as a result of a
recombination operator in a genetic algorithm, given two parent solutions. In
Part II, we consider the computational complexity of ORPs arising in genetic
algorithms for problems on permutations: the Travelling Salesman Problem, the
Shortest Hamilton Path Problem and the Makespan Minimization on Single
Machine and some other related problems. The analysis indicates that the
corresponding ORPs are NP-hard, but solvable by faster algorithms, compared
to the problems they are derived from
- …