We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O(n) time, independent of the number m of edges inserted. For dense DAGs, this is an improvement over the previous best result of O(min{m 3 2 logn, m 3 2 + n logn}) by Katriel and Bodlaender. We also provide an empirical comparison of our algori...

We present an Õ(n)-time algorithm for maintaining the topological order of a directed acyclic graph with n vertices while inserting m edges. This is an improvement over the previous result of O(n) by Ajwani, Friedrich, and Meyer.

We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O(n2.75) time, independent of the number of edges m inserted. For dense DAGs, this is an improvement over the previous best result of O(min{m 3 2 log n,m 32 + n log n}) by Katriel and Bodlaender. We also provide an empirical comparison of our al...

Finding a topological ordering for a directed graph is one of the fundamental problems in computer science. Several textbook-standard algorithms using linear memory have been discovered and utilized to solve several other problems for many decades, especially in resolving dependencies and solving other graph connectivity problems. However, these algorithms are becoming less practical nowadays a...

We propose a method for a parallel implementation of the Self-Organizing Map (SOM) algorithm, widely used in data-mining. We call this method Hybrid in the sense that it combines the advantages of the common network-partition and data-partition approaches, and is particularly effective when dealing with large maps. Based on the fact that a global topological ordering of the map is achieved in a...

The dynamic topological order problem is that of efficiently updating a topological order after an edge insertion. This can be solved using a standard topological sort algorithm in O(v+e+b) time, for a batch of b edge insertions. However, this always traverses the entire graph when processing a batch of insertions, even if only a few edges are added. Dynamic topological order algorithms travers...

This paper introduces an algorithm for determining data clusters called TILO/PRC (Topologically Intrinsic Lexicographic Ordering/Pinch Ratio Clustering). The theoretical foundation for this algorithm, developed in [14], uses ideas from topology (particularly knot theory) suggesting that it should be very flexible and robust with respect to noise. The TILO portion of the algorithm progressively ...

In this paper the basic principles and developments of an unsu-pervised learning algorithm, the Self-Organizing Map (SOM) and a supervised learning algorithm, the Learning Vector Quantization (LVQ) are explained. Some practical applications of the algorithms in data analysis, data visual-ization and pattern recognition tasks are mentioned. In the end of the paper new results are reported about ...

This study aims to deal with a more realistic combined problem of project scheduling and material ordering. The goal is to minimize the total material holding and ordering costs by determining the starting time of activities along with material ordering schedules subject to some constraints. The problem is first mathematically modelled. Then a hybrid simulated annealing and genetic algorithm is...

This paper investigates a self-organizing map algorithm which is simultaneously given multiple inputs, and introduces a criterion of ordering process as the twist measurement for reference vectors in multidimensional array. The self-organizing algorithm and the criterion are termed the parallel self-organizing algorithm and the index of twist, respectively. The algorithm updates reference vecto...