scholarly journals Dynamic Shapley Value in the Game with Perishable Goods

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.

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.

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

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%.

scholarly journals Generalized minimum spanning tree games

2015 ◽  
Vol 4 (2) ◽  
pp. 167-188 ◽  
Author(s):  
Phuoc Hoang Le ◽  
Tri-Dung Nguyen ◽  
Tolga Bektaş
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Generalized Minimum Spanning Tree ◽  
Tree Games

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

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.

scholarly journals Network Connectivity Game

2021 ◽  
Vol 28 (2) ◽  
pp. 73-87
Keyword(s):  
Spanning Tree ◽  
Cost Allocation ◽  
Network Connectivity ◽  
Minimum Cost ◽  
Common Source ◽  
Network Nodes ◽  
Network Cost ◽  
Cost Efficient ◽  
The Cost ◽  
Tree Games

We investigate the cost allocation strategy associated with the problem of providing service /communication between all pairs of network nodes. There is a cost associated with each link and the communication between any pair of nodes can be delivered via paths connecting those nodes. The example of a cost efficient solution which could provide service for all node pairs is a (non-rooted) minimum cost spanning tree. The cost of such a solution should be distributed among users who might have conflicting interests. The objective of this paper is to formulate the above cost allocation problem as a cooperative game, to be referred to as a Network Connectivity (NC) game, and develop a stable and efficient cost allocation scheme. The NC game is related to the Minimum Cost Spanning Tree games and to the Shortest Path games. The profound difference is that in those games the service is delivered from some common source node to the rest of the network, while in the NC game there is no source and the service is established through the two-way interaction among all pairs of participating nodes. We formulate Network Connectivity (NC) game and construct an efficient cost allocation algorithm which finds some points in the core of the NC game. Finally, we discuss the Egalitarian Network Cost Allocation (ENCA) rule and demonstrate that it finds an additional core point.

scholarly journals The Lower Tail of the Random Minimum Spanning Tree

10.37236/1004 ◽  
2007 ◽  
Vol 14 (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, $\log {\rm Pr}[Z \leq \zeta(3) - \varepsilon] = -\Theta(n)$.

scholarly journals Dynamic minimum spanning tree construction and maintenance for Wireless Sensor Networks

2019 ◽  
pp. 57-69
Author(s):  
Sergio Diaz ◽  
Diego Mendez
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Dynamic Networks ◽  
Convergence Time ◽  
Wireless Sensor ◽  
Neighbor Discovery ◽  
Channel Quality ◽  
Tree Construction ◽  
Depth Analysis ◽  
The Cost

In a wireless sensor network (WSN), finding the optimal route from each node to the sink is not a straightforward task because of the distributed and dynamic characteristics of the network. For instance, the network suffers frequent changes because the channel quality varies over time and the nodes can leave or join the network at any moment. In order to deal with this variability, we propose the Dynamic Gallager-Humblet-Spira (DGHS) algorithm that builds and maintains a minimum spanning tree for distributed and dynamic networks, and we have found that DGHS reduces the number of control messages and the energy consumption, at the cost of a slight increase in the memory size and convergence time. This paper presents a detailed description of the different stages of the DGHS algorithm (neighbor discovery, tree construction and data collection), an in-depth analysis of extensive results that validates our proposal, and an exhaustive description of the GHS limitations.

scholarly journals An Approach of Community Search with Minimum Spanning Tree Based on Node Embedding

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jinglian Liu ◽  
Daling Wang ◽  
Shi Feng ◽  
Yifei Zhang
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Search Algorithm ◽  
Feature Representation ◽  
Graph Structure ◽  
Detection Problem ◽  
Second Stage ◽  
Community Search ◽  
Definition Of ◽  
Low Dimensional

Community search is a query-oriented variant of community detection problem, and the goal is to retrieve a single community from a given set of nodes. Most of the existing community search methods adopt handcrafted features, so there are some limitations in applications. Our idea is motivated by the recent advances of node embedding. Node embedding uses deep learning method to obtain feature representation of nodes directly from graph structure automatically and offers a new method to measure the distance between two nodes. In this paper, we propose a two-stage community search algorithm with a minimum spanning tree strategy based on node embedding. At the first stage, we propose a node embedding model NEBRW and map nodes to the points in a low-dimensional vector space. At the second stage, we propose a new definition of community from the distance viewpoint, transform the problem of community search to a variant of minimum spanning tree problem, and uncover the target community with an improved Prim algorithm. We test our algorithm on both synthetic and real-world network datasets. The experimental results show that our algorithm is more effective for community search than baselines.

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