Variable neighborhood search for the cost constrained minimum label spanning tree and label constrained minimum spanning tree problems

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.

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A Low Cost MST-FSM Obfuscation Method for Hardware IP Protection

Journal of Circuits System and Computers ◽

10.1142/s0218126620502084 ◽

2020 ◽

Vol 29 (13) ◽

pp. 2050208

Author(s):

Yuejun Zhang ◽

Zhao Pan ◽

Pengjun Wang ◽

Xiaowei Zhang

Keyword(s):

Integrated Circuit ◽

Spanning Tree ◽

Minimum Spanning Tree ◽

Hamming Distance ◽

Low Cost ◽

The Arts ◽

Finite State ◽

Ip Cores ◽

Building Program ◽

The Cost

Effective resistance to intellectual property (IP) piracy, overproduction and reverse engineering are becoming more and more necessary in the integrated circuit (IC) supply chain. To protect the hardware, the obfuscation methodology hides the original function by adding a large number of redundant states. However, existing hardware obfuscation approaches have hardware overhead and efficiency of obfuscation limitations. This paper proposed a novel methodology for IP security using the minimum spanning tree finite state machine (MST-FSM) obfuscation. In the minimum spanning tree (MST) algorithm, the Hamming distance defines the cost of obfuscated states. The Kruskal algorithm optimizes the connection relationship of obfuscated states by computing the Hamming distance of the MST-FSM. The proposed MST-FSM is automatically generated and embedded in the hardware IP with the self-building program. Finally, the MST-FSM is applied on the itc99 benchmark circuits and encryption standard IP cores. Compared with other state-of-the-arts, the obfuscation potency is improved by 3.57%, and the average hardware cost is decreased by about 6.01%.

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Optimizing Computer Networks Communication with the Band Collocation Problem: A Variable Neighborhood Search Approach

Electronics ◽

10.3390/electronics9111860 ◽

2020 ◽

Vol 9 (11) ◽

pp. 1860

Author(s):

Isaac Lozano-Osorio ◽

Jesus Sanchez-Oro ◽

Miguel Ángel Rodriguez-Garcia ◽

Abraham Duarte

Keyword(s):

Variable Neighborhood Search ◽

Simulated Annealing Algorithm ◽

Previous Method ◽

Point Of View ◽

Telecommunication Networks ◽

Neighborhood Search ◽

Neighborhood Structures ◽

Bandpass Problem ◽

Search Approach ◽

The Cost

The Band Collocation Problem appears in the context of problems for optimizing telecommunication networks with the aim of solving some concerns related to the original Bandpass Problem and to present a more realistic approximation to be solved. This problem is interesting to optimize the cost of networks with several devices connected, such as networks with several embedded systems transmitting information among them. Despite the real-world applications of this problem, it has been mostly ignored from a heuristic point of view, with the Simulated Annealing algorithm being the best method found in the literature. In this work, three Variable Neighborhood Search (VNS) variants are presented, as well as three neighborhood structures and a novel optimization based on Least Recently Used cache, which allows the algorithm to perform an efficient evaluation of the objective function. The extensive experimental results section shows the superiority of the proposal with respect to the best previous method found in the state-of-the-art, emerging VNS as the most competitive method to deal with the Band Collocation Problem.

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Degree-Constrained k -Minimum Spanning Tree Problem

Complexity ◽

10.1155/2020/7628105 ◽

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.

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Dynamic Shapley Value in the Game with Perishable Goods

Contributions to Game Theory and Management ◽

10.21638/11701/spbu31.2021.20 ◽

2021 ◽

Vol 14 ◽

pp. 273-289

Author(s):

Li Yin ◽

◽

Ovanes Petrosian ◽

Zou Jinying ◽

◽

...

Keyword(s):

Spanning Tree ◽

Minimum Spanning Tree ◽

Time Consistency ◽

Characteristic Functions ◽

Cooperative Behaviour ◽

Second Stage ◽

Perishable Goods ◽

Shapley Values ◽

The Cost ◽

Tree Games

The paper investigates two-stage stochastic minimum spanning tree games with perishable goods. The cooperative behaviour of the players is defined. At each stage, all players jointly take action to construct a network with a cost matrix. At the second stage, a particular player may leave the game, and the probability of this leaving depends on the cooperative behaviour of all players at the first stage. At each stage game, the total cost of the spanning tree is calculated to include the sum of the costs of the contained edges and the cost of the loss of perishable goods expended on that edge of the spanning tree. The characteristic functions in the game are considered, and the dynamic Shapley values are modified. The time consistency of the dynamic Shapley values is studied.

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Pengujian Optimalisasi Jaringan Kabel Fiber Optic Di Universitas Islam Indonesia Menggunakan Minimum Spanning Tree

Jurnal Fourier ◽

10.14421/fourier.2014.31.49-58 ◽

2014 ◽

Vol 3 (1) ◽

pp. 49

Author(s):

Muchammad Abrori ◽

Najib Ubaidillah

Keyword(s):

Spanning Tree ◽

Fiber Optic ◽

Minimum Spanning Tree ◽

Computer Network ◽

Star Topology ◽

Cable Length ◽

Cable Network ◽

Cable Lines ◽

The Cost

Universitas Islam Indonesia (UII) intergrated campus computer network built since 1995. Development of UII integrated campus computer network is using a star topology and fiber optic (FO) cable. Considering that the star topology is the topology that requires a lot of wires, this study was conducted to determine and examine how the application of graph on the FO cable network UII integrated campus in order to minimize the cost, because FO cable network can be modeled by a graph where the buildings as points, while FO cable that connects to each building as a line. This type of research that is used here is a case study, in which data collection by observation, interviews, and documentation. This study used 4 algorithms, that is Kruskal algorithm, Prim, Boruvka and Solin algorithm to find the Minimum Spanning Tree. Based on the research that has been done, the conclution about the troubleshooting steps of optimization UII integrated campus FO cable network based graph theory has been got. From the four algorithms obtained the most optimal results FO cable length 4.700 meters long and is 1.590 meters cable lines. While the results of observations made, it is known that the existing computer network in UII integrated campus has a cable length of 6.120 meters and 2.050 meters long track. The results of the analysis showed that the resulrs of the study 23.2% more optimal than the existing computer networks in UII integrated campus.

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The Lower Tail of the Random Minimum Spanning Tree

The Electronic Journal of Combinatorics ◽

10.37236/1004 ◽

2007 ◽

Vol 14 (1) ◽

Cited By ~ 1

Author(s):

Abraham D. Flaxman

Keyword(s):

Spanning Tree ◽

Minimum Spanning Tree ◽

Large Deviation ◽

Random Variable ◽

Independent Random Variables ◽

Large Deviation Probability ◽

Deviation Probability ◽

Lower Tail ◽

The Subject ◽

The Cost

Consider a complete graph $K_n$ where the edges have costs given by independent random variables, each distributed uniformly between 0 and 1. The cost of the minimum spanning tree in this graph is a random variable which has been the subject of much study. This note considers the large deviation probability of this random variable. Previous work has shown that the log-probability of deviation by $\varepsilon$ is $-\Omega(n)$, and that for the log-probability of $Z$ exceeding $\zeta(3)$ this bound is correct; $\log {\rm Pr}[Z \geq \zeta(3) + \varepsilon] = -\Theta(n)$. The purpose of this note is to provide a simple proof that the scaling of the lower tail is also linear, $\log {\rm Pr}[Z \leq \zeta(3) - \varepsilon] = -\Theta(n)$.

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