Recent Results on the Application of a Metric — Space Search Algorithm (AESA) to Multispeaker Data

1988 ◽  
pp. 285-289
Author(s):  
Enrique Vidal ◽  
M. José Lloret
Keyword(s):  
Metric Space ◽  
Search Algorithm

Towards optimal path computation in a simplicial complex

2019 ◽  
Vol 38 (8) ◽  
pp. 981-1009
Author(s):  
Subhrajit Bhattacharya
Keyword(s):  
Simplicial Complex ◽  
Metric Space ◽  
Search Algorithm ◽  
Optimal Path ◽  
Shortest Paths ◽  
Reconstruction Algorithm ◽  
Continuous Space ◽  
Rips Complex ◽  
Geodesic Paths ◽  
Configuration Manifold

Computing optimal path in a configuration space is fundamental to solving motion planning problems in robotics and autonomy. Graph-based search algorithms have been widely used to that end, but they suffer from drawbacks. We present an algorithm for computing the shortest path through a metric simplicial complex that can be used to construct a piece-wise linear discrete model of the configuration manifold. In particular, given an undirected metric graph, G, which is constructed as a discrete representation of an underlying configuration manifold (a larger “continuous” space typically of dimension greater than one), we consider the Rips complex, [Formula: see text], associated with it. Such a complex, and hence shortest paths in it, represent the underlying metric space more closely than what the graph does. Our algorithm requires only a local connectivity-based description of an abstract graph, [Formula: see text], and a cost/length function, [Formula: see text], as inputs. No global information such as an embedding or a global coordinate chart is required. The local nature of the proposed algorithm makes it suitable for configuration spaces of arbitrary topology, geometry, and dimension. We not only develop the search algorithm for computing shortest distances, but we also present a path reconstruction algorithm for explicitly computing the shortest paths through the simplicial complex. The complexity of the presented algorithm is comparable with that of Dijkstra’s search, but, as the results presented in this paper demonstrate, the shortest paths obtained using the proposed algorithm represent the geodesic paths in the original metric space significantly more closely.

On the use of a metric-space search algorithm (AESA) for fast DTW-based recognition of isolated words

1988 ◽  
Vol 36 (5) ◽  
pp. 651-660 ◽  
Author(s):  
E. Vidal ◽  
H.M. Rulot ◽  
F. Casacuberta ◽  
J.-M. Benedi
Keyword(s):  
Metric Space ◽  
Search Algorithm

scholarly journals Indexing algorithm based on storing additional distances in metric space for multi-vantage-point tree

2021 ◽  
pp. 18-27
Author(s):  
Igor Akeksandrov ◽  
Vladimir Fomin
Keyword(s):  
Metric Space ◽  
Similarity Search ◽  
Structural Changes ◽  
Search Algorithm ◽  
Accurate Determination ◽  
Classical Problem ◽  
Search Algorithms ◽  
Vantage Point ◽  
Complex Data ◽  
Access Methods

Introduction: The similarity search paradigm is used in various computational tasks, such as classification, data mining, pattern recognition, etc. Currently, the technology of tree-like metric access methods occupies a significant place among search algorithms. The classical problem of reducing the time of similarity search in metric space is relevant for modern systems when processing big complex data. Due to multidimensional nature of the search algorithm effectiveness problem, local research in this direction is in demand, constantly bringing useful results. Purpose: To reduce the computational complexity of tree search algorithms in problems involving metric proximity. Results: We developed a search algorithm for a multi-vantage-point tree, based on the priority node-processing queue. We mathematically formalized the problems of additional calculations and ways to solve them. To improve the performance of similarity search, we have proposed procedures for forming a priority queue of processing nodes and reducing the number of intersections of same level nodes. Structural changes in the multi-vantage-point tree and the use of minimum distances between vantage points and node subtrees provide better search efficiency. More accurate determination of the distance from the search object to the nodes and the fact that the search area intersects with a tree node allows you to reduce the amount of calculations. Practical relevance: The resulting search algorithms need less time to process information due to an insignificant increase in memory requirements. Reducing the information processing time expands the application boundaries of tree metric indexing methods in search problems involving large data sets.

scholarly journals Metric space method for constructing splitting partitions of graphs

2019 ◽  
Vol 11 (2) ◽  
pp. 131-141
Author(s):  
Sándor Szabó
Keyword(s):  
Metric Space ◽  
Numerical Experiments ◽  
Search Algorithm ◽  
Maximum Clique ◽  
Clique Number ◽  
Maximum Clique Problem ◽  
Branching Rule ◽  
The Given ◽  
Space Method ◽  
Clique Problem

Abstract In an earlier work [6] the concept of splitting partition of a graph was introduced in connection with the maximum clique problem. A splitting partition of a graph can be used to replace the graph by two smaller graphs in the course of a clique search algorithm. In other words splitting partitions can serve as a branching rule in an algorithm to compute the clique number of a given graph. In the paper we revisit this branching idea. We will describe a technique to construct not necessary optimal splitting partitions. The given graph can be viewed as a metric space and the geometry of this space plays a guiding role. In order to assess the performance of the procedure we carried out numerical experiments.

Optimal broadcast scheduling method for VANETs: An adaptive discrete firefly approach

2020 ◽  
Vol 39 (6) ◽  
pp. 8125-8137
Author(s):  
Jackson J Christy ◽  
D Rekha ◽  
V Vijayakumar ◽  
Glaucio H.S. Carvalho
Keyword(s):  
Intelligent Transportation System ◽  
Search Algorithm ◽  
Mac Protocol ◽  
High Mobility ◽  
Optimal Solution ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Traffic Density ◽  
Scheduling Problem ◽  
Broadcast Scheduling

Vehicular Adhoc Networks (VANET) are thought-about as a mainstay in Intelligent Transportation System (ITS). For an efficient vehicular Adhoc network, broadcasting i.e. sharing a safety related message across all vehicles and infrastructure throughout the network is pivotal. Hence an efficient TDMA based MAC protocol for VANETs would serve the purpose of broadcast scheduling. At the same time, high mobility, influential traffic density, and an altering network topology makes it strenuous to form an efficient broadcast schedule. In this paper an evolutionary approach has been chosen to solve the broadcast scheduling problem in VANETs. The paper focusses on identifying an optimal solution with minimal TDMA frames and increased transmissions. These two parameters are the converging factor for the evolutionary algorithms employed. The proposed approach uses an Adaptive Discrete Firefly Algorithm (ADFA) for solving the Broadcast Scheduling Problem (BSP). The results are compared with traditional evolutionary approaches such as Genetic Algorithm and Cuckoo search algorithm. A mathematical analysis to find the probability of achieving a time slot is done using Markov Chain analysis.

Generalized multivalued integral type contraction on weak partial metric space

2020 ◽  
Vol 13 (3) ◽  
pp. 145-151
Author(s):  
Öztürk zlem Acar ◽  
Sümeyye Coşkun
Keyword(s):  
Metric Space ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Integral Type ◽  
Type Contraction
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