An Implementation of Ray Tracing Algorithm for the Multiprocessor Machines
This note is concerned with the bicriteria scheduling problem on a series-batching machine to minimize maximum cost and makespan. An O(n5) algorithm has been established previously. Here is an improved algorithm which solves the problem in O(n3) time.
Many real-world scheduling problems can be modeled as Multi-mode Resource Constrained Project Scheduling Problems (MRCPSP). However, the MRCPSP is a strong NP-hard problem and very difficult to be solved. The purpose of this research is to investigate a more efficient alternative based on ant algorithm to solve MRCPSP. To enhance the generality along with efficiency of the algorithm, the rule pool is designed to manage numerous priority rules for MRCPSP. Each ant is provided with an independent...
A vertex i of a graph G = (V,E) is said to be controlled by if the majority of the elements of the neighborhood of i (including itself) belong to M. The set M is a monopoly in G if every vertex is controlled by M. Given a set and two graphs G1 = () and G2 = () where , the monopoly verification problem (mvp) consists of deciding whether there exists a sandwich graph G = (V,E) (i.e., a graph where ) such that M is a monopoly in G = (V,E). If the answer to the mvp is No, we then consider...
A vertex i of a graph G = (V,E) is said to be controlled by if the majority of the elements of the neighborhood of i (including itself) belong to M. The set M is a monopoly in G if every vertex is controlled by M. Given a set and two graphs G1 = () and G2 = () where , the monopoly verification problem (mvp) consists of deciding whether there exists a sandwich graph G = (V,E) (i.e., a graph where ) such that M is a monopoly in G = (V,E). If the answer to the mvp is No, we then consider...
The concept of usability of man-machine interfaces is usually judged in terms of a number of aspects or attributes that are known to be subject to some rough correlations, and that are in many cases given different importance, depending on the context of use of the application. In consequence, the automation of judgment processes regarding the overall usability of concrete interfaces requires the design of aggregation operators that are capable of modeling approximate or ill-defined interactions...
Here is presented a 6-states non minimal-time solution which is intrinsically Minsky-like and solves the three following problems: unrestricted version on a line, with one initiator at each end of a line and the problem on a ring. We also give a complete proof of correctness of our solution, which was never done in a publication for Minsky's solutions.
This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis, contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics....