Linial's Lower Bound Made Easy

Leveraging Linial's Locality Limit

In this paper we extend the lower bound technique by Linial for local coloring and maximal independent sets. We show that constant approximations to maximum independent sets on a ring require at least log-star time. More generally, the product of approximation quality and running time cannot be less than log-star. Using a generalized ring topology, we gain identical lower bounds for approximati...

Minimizing Makespan with Start Time Dependent Jobs in a Two Machine Flow Shop

[if gte mso 9]> The purpose of this paper is to consider the problem of scheduling a set of start time-dependent jobs in a two-machine flow shop, in which the actual processing times of jobs increase linearly according to their starting time. The objective of this problem is to minimize the makespan. The problem is known to be NP-hardness[ah1] ; therefore, there is no polynomial-time algorithm...

A New Lower Bound for Completion Time Distribution Function of Stochastic PERT Networks

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

A New Lower Bound for Completion Time Distribution Function of Stochastic PERT Networks

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces