In various research papers, such as [2], one will find the claim that the minLA is optimally solvable on outerplanar graphs, with a reference to [1]. However, the problem solved in that publication, which we refer to as the planar minLA, is different from the minLA, as we show in this article. In constrast to the minimum linear arrangement problem (minLA), the planar minimum linear arrangement ...

This paper studies the arrangement problem of uniform trees and shows that the arrangement complexity of a uniform tree is either (1) or ((lg n))(> 0). It also presents a recursive algorithm to compute the optimal complete arrangements for (1) arrangeable balanced uniform trees.

In this paper, we propose a distributed broadcasting algorithm with optimal time complexity and without message redundancy for one-toall broadcasting in the one-port communication model on arrangement graph interconnection networks. The algorithm exploits the hierarchical property of the arrangement graph to construct different-sized broadcasting trees for different-sized subgraphs. These diffe...

The bipartite crossing number problem is studied, and a connection between this problem and the linear arrangement problem is established. It is shown that when the arboricity is close to the minimum degree and the graph is not too sparse, then the optimal number of crossings has the same order of magnitude as the optimal arrangement value times the arboricity. The application of the results to...

Automatic generation of guitar tablatures for given songs has been one of research interests in music information processing. Furthermore, some of recent studies have attempted automatic arrangement of given songs before tablature generation for producing guitar scores for songs composed for other instruments. In our previous work, we have formulated “fingering decision” and “arrangement” in a ...

We give the first efficient parallel algorithms for solving the arrangement problem. We give a deterministic algorithm for the CREW PRAM which runs in nearly optimal bounds of O(log n log∗ n) time and n2/ log n processors. We generalize this to obtain an O(log n log∗ n)-time algorithm using nd / log n processors for solving the problem in d dimensions. We also give a randomized algorithm for th...

Tensor contractions are important computations for many domains including quantum chemistry and big-data applications. Distributed-memory architectures, architectures where numerous processing elements have private memory, are used in order to solve large problems efficiently. On such systems, achieving high performance computation is dependent on the arrangement of the processing elements. The...