We give a random class of lattices in Z n so that, if there is a probabilistic polynomial time algorithm which nds a short vector in a random lattice with a probability of at least 1 2 then there is also a probabilistic polynomial time algorithm which solves the following three lattice problems in every lattice in Z n with a probability exponentially close to one. (1) Find the length of a short...

There exist a number of problem classes for which obtaining the exact solution becomes exponentially expensive with increasing problem size. The quadratic assignment problem (QAP) or the travelling salesman problem (TSP) are just two examples of such NP-hard problems. In practice, approximate algorithms are employed to obtain a suboptimal solution, where one must face a trade-off between comput...

We discuss how phase-transitions may be detected in computationally hard problems in the context of Anytime Algorithms. Treating the computational time, value and utility functions involved in the search results in analogy with quantities in statistical physics, we indicate how the onset of a computationally hard regime can be detected and the transit to higher quality solutions be quantified b...

assigning facilities to locations is one of the important problems, which significantly is influence in transportation cost reduction. in this study, we solve quadratic assignment problem (qap), using a meta-heuristic algorithm with deterministic tasks and equality in facilities and location number. it should be noted that any facility must be assign to only one location. in this paper, first o...

in this paper, a single machine sequencing problem is considered in order to find the sequence of jobs minimizing the sum of the maximum earliness and tardiness with idle times (n/1/i/etmax). due to the time complexity function, this sequencing problem belongs to a class of np-hard ones. thus, a special design of a simulated annealing (sa) method is applied to solve such a hard problem. to comp...