Efficient Incremental Algorithm for Building Swiftly Concepts Lattices

2014 ◽  
Vol 6 (1) ◽  
pp. 21-34 ◽  
Author(s):  
Bakhta Amrane ◽  
Ghalem Belalem ◽  
Sarra Branci ◽  
Yahya Slimani
Keyword(s):  
Experimental Study ◽  
Time Complexity ◽  
Essential Role ◽  
Concept Lattice ◽  
Dynamic Environment ◽  
Algorithmic Complexity ◽  
Incremental Algorithm ◽  
Efficient Tool ◽  
Worst Case ◽  
Formal Concepts

Efficient tool and platform for several areas, concept lattice are widely used in many fields of research. Dynamic environment requires an incremental algorithm to build formal concepts. It plays an essential role in the application of concept lattice. This paper presents a fast, efficient, incremental algorithm to compute formal concepts. Algorithmic complexity is studied both theoretically (in the worst case) and experimentally. It presents a complexity of at most (|M|.|G|.|L|) where M is set of attributes, G is set of objects and L is set of concepts of the lattice. Irrespective of the lattice, the algorithm computes incrementally all formal concepts without increasing time complexity. Algorithmic complexity of the most important incremental algorithms is compared theoretically, and an experimental study based on density/ sparseness of underlying formal contexts is performed with Norris' algorithm classified the most one efficient incremental in practice.

scholarly journals An Incremental Algorithm for Concept Lattice Based on SSIM

2021 ◽  
Author(s):  
Yu Hu ◽  
Yan Zhu Hu ◽  
Zhong Su ◽  
Xiao Li Li ◽  
Zhen Meng ◽  
...  
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Formal Concept Analysis ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Concept Lattice ◽  
Incremental Algorithm ◽  
Formal Concept ◽  
Image Structure ◽  
Structure Similarity

Abstract As an effective tool for data analysis, Formal Concept Analysis (FCA) is widely used in software engineering and machine learning. The construction of concept lattice is a key step of the FCA. How to effectively update the concept lattice is still an open, interesting and important issue. The main aim of this paper is to provide a solution to this problem. So, we propose an incremental algorithm for concept lattice based on image structure similarity (SsimAddExtent). In addition, we perform time complexity analysis and experiments to show effectiveness of algorithm.

scholarly journals Feature Recognition for Manufacturability Analysis

1994 ◽  
Author(s):  
William C. Regli ◽  
Satyandra K. Gupta ◽  
Dana S. Nau
Keyword(s):  
Time Complexity ◽  
Material Removal ◽  
Feature Recognition ◽  
Solid Modeling ◽  
Cad Model ◽  
Worst Case ◽  
Machining Features ◽  
Automated Recognition ◽  
Wide Range ◽  
Complete Set

Abstract While automated recognition of features has been attempted for a wide range of applications, no single existing approach possesses the functionality required to perform manufacturability analysis. In this paper, we present a methodology for taking a CAD model of a part and extracting a set of machinable features that contains the complete set of alternative interpretations of the part as collections of MRSEVs (Material Removal Shape Element Volumes, a STEP-based library of machining features). The approach handles a variety of features including those describing holes, pockets, slots, and chamfering and filleting operations. In addition, the approach considers accessibility constraints for these features, has an worst-case algorithmic time complexity quadratic in the number of solid modeling operations, and modifies features recognized to account for available tooling and produce more realistic volumes for manufacturability analysis.

The construction of multi-granularity concept lattices

2020 ◽  
Vol 39 (3) ◽  
pp. 2783-2790
Author(s):  
Qian Hu ◽  
Ke-Yun Qin
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Mutual Transformation ◽  
Concept Lattices ◽  
Construction Methods ◽  
Formal Concepts ◽  
Transformation Methods

The construction of concept lattices is an important research topic in formal concept analysis. Inspired by multi-granularity rough sets, multi-granularity formal concept analysis has become a new hot research issue. This paper mainly studies the construction methods of concept lattices in multi-granularity formal context. The relationships between concept forming operators under different granularity are discussed. The mutual transformation methods of formal concepts under different granularity are presented. In addition, the approaches of obtaining coarse-granularity concept lattice by fine-granularity concept lattice and fine-granularity concept lattice by coarse-granularity concept lattice are examined. The related algorithms for generating concept lattices are proposed. The practicability of the method is illustrated by an example.

scholarly journals A New Rapid Incremental Algorithm for Constructing Concept Lattices

Information ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 78 ◽  
Author(s):  
Jingpu Zhang ◽  
Ronghui Liu ◽  
Ligeng Zou ◽  
Licheng Zeng
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Incremental Algorithm ◽  
Formal Context ◽  
Formal Concept ◽  
Concept Lattices ◽  
Covering Relation ◽  
Canonical Generator ◽  
Lattice Construction ◽  
Time And Space Complexity

Formal concept analysis has proven to be a very effective method for data analysis and rule extraction, but how to build formal concept lattices is a difficult and hot topic. In this paper, an efficient and rapid incremental concept lattice construction algorithm is proposed. The algorithm, named FastAddExtent, is seen as a modification of AddIntent in which we improve two fundamental procedures, including fixing the covering relation and searching the canonical generator. The proposed algorithm can locate the desired concept quickly by adding data fields to every concept. The algorithm is depicted in detail, using a formal context to show how the new algorithm works and discussing time and space complexity issues. We also present an experimental evaluation of its performance and comparison with AddExtent. Experimental results show that the FastAddExtent algorithm can improve efficiency compared with the primitive AddExtent algorithm.

Planning the Shortest Path in Cluttered Environments: A Review and a Planar Convex Hull-Based Approach

2019 ◽  
Vol 19 (4) ◽  
Author(s):  
Nafiseh Masoudi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Time Complexity ◽  
Optimal Path ◽  
Optimal Solution ◽  
Free Graph ◽  
Worst Case ◽  
Cluttered Environments ◽  
Planar Convex ◽  
Polyhedral Obstacles

Abstract Routing or path-planning is the problem of finding a collision-free and preferably shortest path in an environment usually scattered with polygonal or polyhedral obstacles. The geometric algorithms oftentimes tackle the problem by modeling the environment as a collision-free graph. Search algorithms such as Dijkstra’s can then be applied to find an optimal path on the created graph. Previously developed methods to construct the collision-free graph, without loss of generality, explore the entire workspace of the problem. For the single-source single-destination planning problems, this results in generating some unnecessary information that has little value and could increase the time complexity of the algorithm. In this paper, first a comprehensive review of the previous studies on the path-planning subject is presented. Next, an approach to address the planar problem based on the notion of convex hulls is introduced and its efficiency is tested on sample planar problems. The proposed algorithm focuses only on a portion of the workspace interacting with the straight line connecting the start and goal points. Hence, we are able to reduce the size of the roadmap while generating the exact globally optimal solution. Considering the worst case that all the obstacles in a planar workspace are intersecting, the algorithm yields a time complexity of O(n log(n/f)), with n being the total number of vertices and f being the number of obstacles. The computational complexity of the algorithm outperforms the previous attempts in reducing the size of the graph yet generates the exact solution.

scholarly journals TIME OPTIMAL ALGORITHMS FOR BLACK HOLE SEARCH IN RINGS

2011 ◽  
Vol 03 (04) ◽  
pp. 457-471 ◽  
Author(s):  
B. BALAMOHAN ◽  
P. FLOCCHINI ◽  
A. MIRI ◽  
N. SANTORO
Keyword(s):  
Black Hole ◽  
Time Complexity ◽  
Time Cost ◽  
Ring Networks ◽  
Worst Case ◽  
Average Case ◽  
Case Complexity ◽  
Average Case Complexity ◽  
Time Optimal ◽  
Optimal Average

In a network environment supporting mobile entities (called robots or agents), a black hole is a harmful site that destroys any incoming entity without leaving any visible trace. The black-hole search problit is the task of a team of k > 1 mobile entities, starting from the same safe location and executing the same algorithm, to determine within finite time the location of the black hole. In this paper, we consider the black hole search problit in asynchronous ring networks of n nodes, and focus on time complexity. It is known that any algorithm for black-hole search in a ring requires at least 2(n - 2) time in the worst case. The best known algorithm achieves this bound with a team of n - 1 agents with an average time cost of 2(n - 2), equal to the worst case. In this paper, we first show how the same number of agents using 2 extra time units in the worst case, can solve the problit in only [Formula: see text] time on the average. We then prove that the optimal average case complexity of [Formula: see text] can be achieved without increasing the worst case using 2(n - 1) agents. Finally, we design an algorithm that achieves asymptotically optimal both worst and average case time complexities itploying an optimal team of k = 2 agents, thus improving on the earlier results that required O(n) agents.

scholarly journals On Rectilinear Distance-Preserving Trees

VLSI Design ◽  
1998 ◽  
Vol 7 (1) ◽  
pp. 15-30
Author(s):  
Gustavo E. Téllez ◽  
Majid Sarrafzadeh
Keyword(s):  
Approximation Algorithm ◽  
Heuristic Algorithm ◽  
Time Complexity ◽  
High Performance ◽  
Exact Algorithm ◽  
Wire Length ◽  
Worst Case ◽  
Rectilinear Distance ◽  
Source To Sink ◽  
Linear Delay

Given a set of terminals on the plane N={s,ν1,…,νn}, with a source terminal s, a Rectilinear Distance-Preserving Tree (RDPT) T(V, E) is defined as a tree rooted at s, connecting all terminals in N. An RDPT has the property that the length of every source to sink path is equal to the rectilinear distance between that source and sink. A Min- Cost Rectilinear Distance-Preserving Tree (MRDPT) minimizes the total wire length while maintaining minimal source to sink linear delay, making it suitable for high performance interconnect applications.This paper studies problems in the construction of RDPTs, including the following contributions. A new exact algorithm for a restricted version of the problem in one quadrant with O(n2) time complexity is proposed. A novel heuristic algorithm, which uses optimally solvable sub-problems, is proposed for the problem in a single quadrant. The average and worst-case time complexity for the proposed heuristic algorithm are O(n3/2) and O(n3), respectively. A 2-approximation of the quadrant merging problem is proposed. The proposed algorithm has time complexity O(α2T(n)+α3) for any constant α > 1, where T(n) is the time complexity of the solution of the RDPT problem on one quadrant. This result improves over the best previous quadrant merging solution which has O(n2T(n)+n3) time complexity.We test our algorithms on randomly uniform point sets and compare our heuristic RDPT construction against a Minimum Cost Rectilinear Steiner (MRST) tree approximation algorithm. Our results show that RDPTs are competitive with Steiner trees in total wire-length when the number of terminals is less than 32. This result makes RDPTs suitable for VLSI routing applications. We also compare our algorithm to the Rao-Shor RDPT approximation algorithm obtaining improvements of up to 10% in total wirelength. These comparisons show that the algorithms proposed herein produce promising results.

Multi-Relational Sequential Pattern Mining Based on Iceberg Concept Lattice

2011 ◽  
Vol 109 ◽  
pp. 729-733
Author(s):  
Jiang Yin ◽  
Yun Li ◽  
Cen Cheng Shen ◽  
Bo Liu
Keyword(s):  
Data Mining ◽  
Time Complexity ◽  
Pattern Mining ◽  
Concept Lattice ◽  
Optimization Methods ◽  
Sequential Pattern Mining ◽  
Experimental Results ◽  
Sequential Pattern ◽  
Sequential Mining ◽  
Mining Methods

Multi-Relational Sequential mining is one of the areas of data mining that rapidly developed in recent years. However, the performance issues of traditional mining methods are not ideal. To effectively mining the pattern, we proposed an algorithm based on Iceberg concept lattice, adopting optimization methods of partition and merger to just mining the frequent sequences. Experimental results show this algorithm effectively reduced the time complexity of multi-relational sequential pattern mining.

Sign in / Sign up

Export Citation Format

Share Document