X-architecture Steiner minimal tree algorithm based on multi-strategy optimization discrete differential evolution

Global routing is an important link in very large scale integration (VLSI) design. As the best model of global routing, X-architecture Steiner minimal tree (XSMT) has a good performance in wire length optimization. XSMT belongs to non-Manhattan structural model, and its construction process cannot be completed in polynomial time, so the generation of XSMT is an NP hard problem. In this paper, an X-architecture Steiner minimal tree algorithm based on multi-strategy optimization discrete differential evolution (XSMT-MoDDE) is proposed. Firstly, an effective encoding strategy, a fitness function of XSMT, and an initialization strategy of population are proposed to record the structure of XSMT, evaluate the cost of XSMT and obtain better initial particles, respectively. Secondly, elite selection and cloning strategy, multiple mutation strategies, and adaptive learning factor strategy are presented to improve the search process of discrete differential evolution algorithm. Thirdly, an effective refining strategy is proposed to further improve the quality of the final Steiner tree. Finally, the results of the comparative experiments prove that XSMT-MoDDE can get the shortest wire length so far, and achieve a better optimization degree in the larger-scale problem.

A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

Minimum-cost spanning tree problems are well-known problems in the operations research literature. Some agents, located at different geographical places, want a service provided by a common supplier. Agents will be served through costly connections. Some part of the literature has focused, mainly, in studying how to allocate the connection cost among the agents. We review the papers that have addressed the allocation problem using cooperative game theory. We also relate the rules defined through cooperative games with rules defined directly from the problem, either through algorithms for computing a minimal tree, either through a cone-wise decomposition.

Trees with Minimum Weighted Szeged Index Are of a Large Diameter

The weighted Szeged index ( w S z ) has gained considerable attention recently because of its unusual mathematical properties. Searching for a tree (or trees) that minimizes the w S z is still going on. Several structural details of a minimal tree were described. Here, it is shown a surprising property that these trees have maximum degree at most 16, and as a consequence, we promptly conclude that these trees are of large diameter.

Efficient Inference of Optimal Decision Trees

Inferring a decision tree from a given dataset is a classic problem in machine learning. This problem consists of building, from a labelled dataset, a tree where each node corresponds to a class and a path between the tree root and a leaf corresponds to a conjunction of features to be satisfied in this class. Following the principle of parsimony, we want to infer a minimal tree consistent with the dataset. Unfortunately, inferring an optimal decision tree is NP-complete for several definitions of optimality. For this reason, the majority of existing approaches rely on heuristics, and the few existing exact approaches do not work on large datasets. In this paper, we propose a novel approach for inferring an optimal decision tree with a minimum depth based on the incremental generation of Boolean formulas. The experimental results indicate that it scales sufficiently well and the time it takes to run grows slowly with the size of datasets.

Identifying Brain Region Connectivity using Steiner Minimal Tree Approximation and a Genetic Algorithm

BackgroundComputation and visualization of connectivity among the brain regions is vital for tasks such as disease identification and drug discovery. An effective visualization can aid clinicians and biologists to perform these tasks addressing a genuine research and industrial need. In this paper, we present SMT-Neurophysiology, a web-based tool in a form of an approximation to the Steiner Minimal Tree (SMT) algorithm to search neurophysiology partonomy and connectivity graph in order to find biomedically-meaningful paths that could explain, to neurologists and neuroscientists, the mechanistic relationship, for example, among specific neurophysiological examinations. We also present SMT-Genetic, a web-based tool in a form of a Genetic Algorithm (GA) to find better paths than SMT-Neurophysiology.ResultsWe introduce an approximation to the SMT algorithm to identify the most parsimonious connectivity among the brain regions of interest. We have implemented our algorithm as a highly interactive web application called SMT-Neurophysiology that enables such computation and visualization. It operates on brain region connectivity dataset curated from the Neuroscience Information Framework (NIF) for four species – human, monkey, rat and bird. We present two case studies on finding the most biomedically-meaningful solutions that identifies connections among a set of brain regions over a specific route. The case studies demonstrate that SMT-Neurophysiology is able to find connection among brain regions of interest. Furthermore, SMT-Neurophysiology is modular and generic in nature allowing the underlying connectivity graph to model any data on which the tool can operate. In order to find better connections among a set of brain regions than SMT-Neurophysiology, we have implemented a web-based tool in a form of a GA called SMT-Genetic. We present further three case studies where SMT-Genetic finds better connections among a set of brain regions than SMT-Neurophysiology. SMT-Genetic gives better connections because SMT-Genetic finds global optimum whereas SMT-Neurophysiology finds local optimum although execution time of SMT-Genetic is higher than SMT-Neurophysiology.ConclusionOur analysis would provide key insights to clinical investigators about potential mechanisms underlying a particular neurological disease. The web-based tools and the underlying data are useful to clinicians and scientists to understand neurological disease mechanisms; discover pharmacological or surgical targets; and design diagnostic or therapeutic clinical trials. The source codes and links to the live tools are available at https://github.com/dewancse/connected-brain-regions and https://github.com/dewancse/SMT-Genetic.