scholarly journals Degree-Constrained k -Minimum Spanning Tree Problem

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
Pablo Adasme ◽  
Ali Dehghan Firoozabadi
Keyword(s):  
Learning Strategies ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Learning Strategy ◽  
Learning Algorithm ◽  
Hamiltonian Path ◽  
Minimum Cost ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Q Learning

Let G V , E be a simple undirected complete graph with vertex and edge sets V and E , respectively. In this paper, we consider the degree-constrained k -minimum spanning tree (DC k MST) problem which consists of finding a minimum cost subtree of G formed with at least k vertices of V where the degree of each vertex is less than or equal to an integer value d ≤ k − 2 . In particular, in this paper, we consider degree values of d ∈ 2,3 . Notice that DC k MST generalizes both the classical degree-constrained and k -minimum spanning tree problems simultaneously. In particular, when d = 2 , it reduces to a k -Hamiltonian path problem. Application domains where DC k MST can be adapted or directly utilized include backbone network structures in telecommunications, facility location, and transportation networks, to name a few. It is easy to see from the literature that the DC k MST problem has not been studied in depth so far. Thus, our main contributions in this paper can be highlighted as follows. We propose three mixed-integer linear programming (MILP) models for the DC k MST problem and derive for each one an equivalent counterpart by using the handshaking lemma. Then, we further propose ant colony optimization (ACO) and variable neighborhood search (VNS) algorithms. Each proposed ACO and VNS method is also compared with another variant of it which is obtained while embedding a Q-learning strategy. We also propose a pure Q-learning algorithm that is competitive with the ACO ones. Finally, we conduct substantial numerical experiments using benchmark input graph instances from TSPLIB and randomly generated ones with uniform and Euclidean distance costs with up to 400 nodes. Our numerical results indicate that the proposed models and algorithms allow obtaining optimal and near-optimal solutions, respectively. Moreover, we report better solutions than CPLEX for the large-size instances. Ultimately, the empirical evidence shows that the proposed Q-learning strategies can bring considerable improvements.

scholarly journals Algorithms for the power-p Steiner tree problem in the Euclidean plane

2018 ◽  
Vol 25 (4) ◽  
pp. 28
Author(s):  
Christina Burt ◽  
Alysson Costa ◽  
Charl Ras
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Valid Inequalities ◽  
Minimum Cost ◽  
Performance Ratio ◽  
Mixed Integer ◽  
Steiner Tree Problem ◽  
Steiner Points ◽  
Tree Construction ◽  
The Cost

We study the problem of constructing minimum power-$p$ Euclidean $k$-Steiner trees in the plane. The problem is to find a tree of minimum cost spanning a set of given terminals where, as opposed to the minimum spanning tree problem, at most $k$ additional nodes (Steiner points) may be introduced anywhere in the plane. The cost of an edge is its length to the power of $p$ (where $p\geq 1$), and the cost of a network is the sum of all edge costs. We propose two heuristics: a ``beaded" minimum spanning tree heuristic; and a heuristic which alternates between minimum spanning tree construction and a local fixed topology minimisation procedure for locating the Steiner points. We show that the performance ratio $\kappa$ of the beaded-MST heuristic satisfies $\sqrt{3}^{p-1}(1+2^{1-p})\leq \kappa\leq 3(2^{p-1})$. We then provide two mixed-integer nonlinear programming formulations for the problem, and extend several important geometric properties into valid inequalities. Finally, we combine the valid inequalities with warm-starting and preprocessing to obtain computational improvements for the $p=2$ case.

scholarly journals FUZZY SHORTEST ROUTE ALGORITHM FOR TELEPHONE LINE CONNECTION USING THE LC-MST ALGORITHM

2015 ◽  
Vol 2 (2) ◽  
pp. 37-39
Author(s):  
Vijayalakshmi D ◽  
Kalaivani R
Keyword(s):  
Transmission Lines ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Minimum Cost ◽  
Distribution Networks ◽  
Minimum Length ◽  
Fuzzy Graph ◽  
Telephone Line ◽  
Water Pipelines ◽  
Communication Links

In computer science, there are many algorithms that finds a minimum spanning tree for a connected weighted undirected fuzzy graph. The minimum length (or cost) spanning tree problem is one of the nicest and simplest problems in network optimization, and it has a wide variety of applications. The problem is tofind a minimum cost (or length) spanning tree in G. Applications include the design of various types of distribution networks in which the nodes represent cities, centers etc.; and edges represent communication links (fiber glass phone lines, data transmission lines, cable TV lines, etc.), high voltage power transmissionlines, natural gas or crude oil pipelines, water pipelines, highways, etc. The objective is to design a network that connects all the nodes using the minimum length of cable or pipe or other resource in this paper we find the solution to the problem is to minimize the amount of new telephone line connection using matrixalgorithm with fuzzy graph.

scholarly journals Resource allocation in clustered M2M networks: a q-learning approach

2021 ◽  
Author(s):  
Fatima Hussain
Keyword(s):  
Resource Allocation ◽  
Learning Algorithm ◽  
Random Access ◽  
Cumulative Distribution ◽  
Convergence Time ◽  
Mixed Integer ◽  
M2m Communication ◽  
Q Learning ◽  
Threshold Levels ◽  
Slot Assignment

Machine to machine (M2M) communication has received increasing attention in recent years. A M2M network exhibits salient features such as large number of machines/devices, low data rates, delay tolerant/sensitive, small sized packets, energy-constrained and low or no mobility. A large number of M2M terminals may exist in a small area with many trying to simultaneously and randomly access for channel resources - which will result in overload and access problem. This increased signaling overhead and diverse requirements of machine type communication devices (MTCDs) call for the development of flexible and efficient scheduling and random access techniques. In this thesis, we first review and compare various scheduling and random access techniques in LTE-based cellular networks for M2M communication. We also discuss how successful they are to fulfill the unique requirements of M2M communication and networking. Resource management in M2M networks with a large number devices is also reviewed from the access point of view. We propose a multi-objective optimization based solution to the problem of resource allocation in interference-limited M2M communication. We consider MTCDs in a clustered network structure, where they are divided into clusters and the devices belonging to a cluster communicate to cluster head (or controller). We maximize the number of admitted MTCD controllers and throughput with least interference caused to conventional primary users. We formulate the problem as a mixed-integer non-linear problem with multiple objectives and solve it using meshed adaptive direct search (MADS) algorithm. Simulation results show the effects of varying different parameters on cumulative throughput and the number of admitted iii MTCD controllers. We then formulate the slot selection problem in M2M networks with admitted MTCDs as an optimization problem. We present a solution using the Q-learning algorithm to select conflict-free slot assignment in a random access network with MTCD controllers. The performance of the solution is dependent on parameters such as learning rate and reward. We thoroughly analyze the performance of the proposed algorithm considering different parameters related to its operation. We also compare it with simple ALOHA and channel-based scheduled allocation and show that the proposed Q-learning based technique has a higher probability of assigning slots compared to these techniques. We then present a block based Q-learning algorithm for the scheduling of MTCDs in clustered M2M communication networks. At first centralized slot assignment is done and an algorithm is proposed for minimizing the inter-cluster interference. Then we propose to use an Q-learning algorithm to assign slots in a distributed manner and comparison is made between the two schemes. Afterwards, we show the effects of distributed slot-assignment with respect to varying signal-to-interference ratio on convergence rate and convergence probability. Cumulative distribution function is used to study the effect of various SIR threshold levels on the convergence probability. With the increase in SIR threshold levels, increase in convergence time and decrease in convergence probability are observed, as less block configuration fulfills the required threshold in the M2M network.

scholarly journals Consistent and powerful non-Euclidean graph-based change-point test with applications to segmenting random interfered video data

2018 ◽  
Vol 115 (23) ◽  
pp. 5914-5919 ◽  
Author(s):  
Xiaoping Shi ◽  
Yuehua Wu ◽  
Calyampudi Radhakrishna Rao
Keyword(s):  
Change Point ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Hamiltonian Path ◽  
Video Data ◽  
Change Point Detection ◽  
Change Point Test ◽  
Point Test ◽  
Point Detection

The change-point detection has been carried out in terms of the Euclidean minimum spanning tree (MST) and shortest Hamiltonian path (SHP), with successful applications in the determination of authorship of a classic novel, the detection of change in a network over time, the detection of cell divisions, etc. However, these Euclidean graph-based tests may fail if a dataset contains random interferences. To solve this problem, we present a powerful non-Euclidean SHP-based test, which is consistent and distribution-free. The simulation shows that the test is more powerful than both Euclidean MST- and SHP-based tests and the non-Euclidean MST-based test. Its applicability in detecting both landing and departure times in video data of bees’ flower visits is illustrated.

GRAPH-BASED ORDERING SCHEME FOR COLOR IMAGE FILTERING

2008 ◽  
Vol 08 (03) ◽  
pp. 473-493 ◽  
Author(s):  
O. LEZORAY ◽  
C. MEURIE ◽  
A. ELMOATAZ
Keyword(s):  
Complete Graph ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Extreme Values ◽  
Color Image ◽  
Hamiltonian Path ◽  
Image Filtering ◽  
Second Step ◽  
Median Filtering ◽  
Step Algorithm

This paper presents a graph-based ordering scheme of color vectors. A complete graph is defined over a filter window and its structure is analyzed to construct an ordering of color vectors. This graph-based ordering is constructed by finding a Hamiltonian path across the color vectors of a filter window by a two-step algorithm. The first step extracts, by decimating a minimum spanning tree, the extreme values of the color set. These extreme values are considered as the infimum and the supremum of the set of color vectors. The second step builds an ordering by constructing a Hamiltonian path among the vectors of color vectors, starting from the infimum and ending at the supremum. The properties of the proposed graph-based ordering of vectors are detailed. Several experiments are conducted to assess its filtering abilities for morphological and median filtering.

scholarly journals Teaching Robots to Interact with Humans in a Smart Environment

2019 ◽  
Author(s):  
Shivam Goel
Keyword(s):  
Network Architecture ◽  
Learning Strategy ◽  
Learning Algorithm ◽  
Primary Objective ◽  
Human Robot Interaction ◽  
Neural Network Architecture ◽  
Robot Interaction ◽  
Q Learning ◽  
The Individual ◽  
And Robotics

Robotics in healthcare has recently emerged, backed by the recent advances in the field of machine learning and robotics. Researchers are focusing on training robots for interacting with elderly adults. This research primarily focuses on engineering more efficient robots that can learn from their mistakes, thereby aiding in better human-robot interaction. In this work, we propose a method in which a robot learns to navigate itself to the individual in need. The robotic agents' learning algorithm will be capable of navigating in an unknown environment. The robot's primary objective is to locate human in a house, and upon finding the human, the goal is to interact with them while complementing their pose and gaze. We propose an end to end learning strategy, which uses a recurrent neural network architecture in combination with Q-learning to train an optimal policy. The idea can be a contribution to better human-robot interaction.

scholarly journals Resource allocation in clustered M2M networks: a q-learning approach

2021 ◽  
Author(s):  
Fatima Hussain
Keyword(s):  
Resource Allocation ◽  
Learning Algorithm ◽  
Random Access ◽  
Cumulative Distribution ◽  
Convergence Time ◽  
Mixed Integer ◽  
M2m Communication ◽  
Q Learning ◽  
Threshold Levels ◽  
Slot Assignment

Machine to machine (M2M) communication has received increasing attention in recent years. A M2M network exhibits salient features such as large number of machines/devices, low data rates, delay tolerant/sensitive, small sized packets, energy-constrained and low or no mobility. A large number of M2M terminals may exist in a small area with many trying to simultaneously and randomly access for channel resources - which will result in overload and access problem. This increased signaling overhead and diverse requirements of machine type communication devices (MTCDs) call for the development of flexible and efficient scheduling and random access techniques. In this thesis, we first review and compare various scheduling and random access techniques in LTE-based cellular networks for M2M communication. We also discuss how successful they are to fulfill the unique requirements of M2M communication and networking. Resource management in M2M networks with a large number devices is also reviewed from the access point of view. We propose a multi-objective optimization based solution to the problem of resource allocation in interference-limited M2M communication. We consider MTCDs in a clustered network structure, where they are divided into clusters and the devices belonging to a cluster communicate to cluster head (or controller). We maximize the number of admitted MTCD controllers and throughput with least interference caused to conventional primary users. We formulate the problem as a mixed-integer non-linear problem with multiple objectives and solve it using meshed adaptive direct search (MADS) algorithm. Simulation results show the effects of varying different parameters on cumulative throughput and the number of admitted iii MTCD controllers. We then formulate the slot selection problem in M2M networks with admitted MTCDs as an optimization problem. We present a solution using the Q-learning algorithm to select conflict-free slot assignment in a random access network with MTCD controllers. The performance of the solution is dependent on parameters such as learning rate and reward. We thoroughly analyze the performance of the proposed algorithm considering different parameters related to its operation. We also compare it with simple ALOHA and channel-based scheduled allocation and show that the proposed Q-learning based technique has a higher probability of assigning slots compared to these techniques. We then present a block based Q-learning algorithm for the scheduling of MTCDs in clustered M2M communication networks. At first centralized slot assignment is done and an algorithm is proposed for minimizing the inter-cluster interference. Then we propose to use an Q-learning algorithm to assign slots in a distributed manner and comparison is made between the two schemes. Afterwards, we show the effects of distributed slot-assignment with respect to varying signal-to-interference ratio on convergence rate and convergence probability. Cumulative distribution function is used to study the effect of various SIR threshold levels on the convergence probability. With the increase in SIR threshold levels, increase in convergence time and decrease in convergence probability are observed, as less block configuration fulfills the required threshold in the M2M network.

Sign in / Sign up

Export Citation Format

Share Document