• Journal of KIISE:Computer Systems and Theory
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• v.36 no.3
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• pp.135-139
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• 2009

The problems to compute the distances or similarities of multiple strings have been vigorously studied in such diverse fields as pattern matching, web searching, bioinformatics, computer security, etc. One well-known method to compare multiple strings in the given set is finding a consensus string which is a representative of the given set. There are two objective functions that are frequently used to find a consensus string, one is the radius and the other is the consensus error. The radius of a string x with respect to a set S of strings is the smallest number r such that the distance between the string x and each string in S is at most r. A consensus string based on radius is a string that minimizes the radius with respect to a given set. The consensus error of a string with respect to a given set S is the sum of the distances between x and all the strings in S. A consensus string of S based on consensus error is a string that minimizes the consensus error with respect to S. In this paper, we show that the problem of finding a consensus string based on radius is NP-complete when the distance function is a metric.

• ETRI Journal
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• v.42 no.6
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• pp.872-885
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• 2020

Distributed consensus requires the consent of more than half of the congress to produce irreversible results, and the performance of the consensus algorithm deteriorates with the increase in the number of nodes. This problem can be addressed by delegating the agreement to a few selected nodes. Since the selected nodes must comply with the Byzantine node ratio criteria required by the algorithm, the result selected by any decentralized node cannot be trusted. However, some trusted nodes monopolize the consensus node selection process, thereby breaking decentralization and causing a trilemma. Therefore, a consensus node selection algorithm is required that can construct a congress that can withstand Byzantine faults with the decentralized method. In this paper, an algorithm based on the Byzantine agreement among decentralized agents to facilitate agreement between decentralization nodes is proposed. It selects a group of random consensus nodes per block by applying the proposed proof of nonce algorithm. By controlling the percentage of Byzantine included in the selected nodes, it solves the trilemma when an arbitrary node selects the consensus nodes.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.11
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• pp.1663-1669
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• 2021

This paper considers the cooperative control problem for multiple leaders and a single follower with interactions. The leaders are controllable, and the follower has interactions with all leaders and is controlled by the interactions. Then, we study the cooperative control problem that achieves the consensus by controlling the leaders. The leaders and the follower are modeled by the single-integrator and the double-integrator, respectively, and it is assumed that the interactions have the nonlinearities. The leaders can estimate the interaction between the follower and exchange the estimated information with neighbors. Then, this paper proposes the consensus-based cooperative control algorithm using the information exchange of the estimated interactions and the virtual velocity variables to achieve the velocity consensus. We analyze the convergence of the agents to the common state based on the Lasalle's Invaraince Principle. Finally, we provide the numerical example to validate the theoretical results.

• Education of Primary School Mathematics
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• v.7 no.2
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• pp.117-129
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• 2003

The purpose of this study is to analyze the interaction patterns and the commonly accepted norms of reaching a consensus among small-group children when solving open-ended problems. In conclusion, open-ended problems have various strategies or different acceptable answers, so they give children learning opportunities to compare the answers and to participate in communication. And more valuable interaction patterns come from 'measuring','classifying' problems and open-ended problems with implicit solution. Therefore, teachers might as well consider the relation between problems and interaction patterns when they pose open-ended problems in a small-group study setting. They are expected to empower children to have sociomathematical norms of reaching a consensus un der indirect and supportive guidance.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2001.08a
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• pp.11-35
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• 2001

For the last twenty years fragment assembly in DNA sequencing followed the "overlap - layout - consensus"paradigm that is used in all currently available assembly tools. Although this approach proved to be useful in assembling clones, it faces difficulties in genomic shotgun assembly: the existing algorithms make assembly errors and are often unable to resolve repeats even in prokaryotic genomes. Biologists are well-aware of these errors and are forced to carry additional experiments to verify the assembled contigs. We abandon the classical “overlap - layout - consensus”approach in favor of a new Eulerian Superpath approach that, for the first time, resolves the problem of repeats in fragment assembly. Our main result is the reduction of the fragment assembly to a variation of the classical Eulerian path problem. This reduction opens new possibilities for repeat resolution and allows one to generate error-free solutions of the large-scale fragment assemble problems. The major improvement of EULER over other algorithms is that it resolves all repeats except long perfect repeats that are theoretically impossible to resolve without additional experiments.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.5
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• pp.439-444
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• 2012

In this study, we address the formation control problem of coupled unicycle-type mobile robots, each of which can interact with its neighboring robots by communicating their position outputs. Each communication link between two mobile robots is assumed to be established according to the given time-varying interconnection topology that switches within a finite set of connected fixed undirected networks and has a non-vanishing dwell time. Under this setup, we propose a distributed formation control algorithm by using the dynamics extension and feedback linearization methods, and by employing a consensus algorithm for linear multi-agent systems which provides arbitrary fast convergence rate to the agreement of the multi-agent system. Finally, the proposed result is demonstrated through a computer simulation.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.3
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• pp.25-32
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• 2019

The core of the block chain technology is solving the problem of agreement on double payment, and the PoW, PoS and DPoS algorithms used for this have been studied. PoW in-process proofs are consensus systems that require feasible efforts to prevent minor or malicious use of computing capabilities, such as sending spam e-mail or initiating denial of service (DoS) attacks. The proof of the PoS is made to solve the Nothing at stake problem as well as the energy waste of the proof of work (PoW) algorithm, and the decision of the sum of each node is decided according to the amount of money, not the calculation ability. DPoS is that a small number of authorized users maintain a trade consensus through a distributed network, whereas DPS provides consent authority to a small number of representatives, whereas PoS has consent authority to all users. If PoS is direct democracy, DPoS is indirect democracy. This study aims to contribute to the continuous development of the related field through the study of the algorithm of the block chain agreement.

• Journal of KIISE
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• v.42 no.3
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• pp.289-294
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• 2015

The consensus problem is finding a representative string, called a consensus, of a given set S of k strings. Circular strings are different from linear strings in that the last symbol precedes the first symbol. Given a set S of circular strings of length n over an alphabet ${\Sigma}$, we first present an $O({\mid}{\Sigma}{\mid}nlogn)$ time parallel algorithm for finding a consensus of S minimizing both radius and distance sum when k=3 using O(n) threads. Then we present an $O({\mid}{\Sigma}{\mid}n^2logn)$ time parallel algorithm for finding a consensus of S minimizing distance sum when k=4 using O(n) threads. Finally, we compare execution times of our algorithms implemented using CUDA with corresponding sequential algorithms.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.14 no.4
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• pp.284-291
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• 2021

In this paper, we study the consensus problem for multi-agent systems with input saturations. The goal of consensus is to achieve a swarming behavior of multi-agent systems by reaching the agreement through information exchange. This paper considers agents modeled by first-order dynamics with input saturations. In order to guarantee the global convergence of the agents, it is assumed that the agents are stable. Moreover, considering the disturbances, we propose the PI based duplex control method to achieve the consensus. The proposed P controller and I controller are composed of different information network. Then, we investigate the conditions of the information networks and the control gains of P, I controllers to achieve the consensus applying the Lyapunov stability theorem and the Lasalle's Invariance Principle. Finally, we conduct the simulations to validate the theoretical results.

• Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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• v.7 no.2
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• pp.267-277
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• 2017

One of fundamental problems in developing robust distributed services is how to achieve distributed consensus agreeing some data values that should be shared among participants in a distributed service. As one of algorithms for distributed consensus, Raft is known as a simple and understandable algorithm by decomposing the distributed consensus problem into three subproblems(leader election, log replication and safety). But, the algorithm dose not mention any types of dynamic configuration of participant peers such as adding new peers to a consensus group or deleting peers from the group. In this paper, we present a new consensus algorithm named Raft-D, which supports the dynamic configuration of participant peers by extending the Raft algorithm. For this, Raft-D manages the additional information maintained by participant nodes, and provides a technique to check the connection status of the nodes belonging to the consensus group. Based on the technique, Raft-D defines conditions and states to deal with adding new peers to the consensus group or deleting peers from the group. Based on those conditions and states, Raft-D performs the dynamic configuration process for a consensus group through the log update mechanism of the Raft algorithm.