• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.359-366
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• 2014

A three-valued function f defined on the vertices of a digraph D = (V, A), $f:V{\rightarrow}\{-1,0,+1\}$ is a minus total dominating function(MTDF) if $f(N^-(v)){\geq}1$ for each vertex $v{\in}V$. The minus total domination number of a digraph D equals the minimum weight of an MTDF of D. In this paper, we discuss some properties of the minus total domination number and obtain a few lower bounds of the minus total domination number on a digraph D.

• Journal of the Korean Operations Research and Management Science Society
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• v.36 no.2
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• pp.1-14
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• 2011

In this paper, we deal with an access network design problem of fiber-to-the-home passive optical network (FTTH-PON). The FTTH-PON network design problem seeks to minimize the total cost of optical splitters and cables that provide optical connectivity between central office and subscribers. We develop a flow-based mixed integer programming (MIP) model with nonlinear link cost. By developing valid inequalities and preprocessing rules, we enhance the strength of the proposed MIP model in generating tight lower bounds for the problem. We develop an effective Tabu Search (TS) heuristic algorithm that provides good quality feasible solutions to the problem. Computational results demonstrate that the valid inequalities and preprocessing rules are effective for improving the LP-relaxation lower bound and TS algorithm finds good quality solutions within reasonable time bounds.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.1
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• pp.35-49
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• 2008

To load a container in a yard block onto a ship, a Transfer Crane (TC) moves to a target yard bay, then its hoist picks up a selected container and loads it onto a waiting Yard Truck (YT). An optimal routing problem of Transfer Crane is a decision problem which determines a given TC's the visiting sequence of yard-bays and the number of containers to transfer from each yard-bay. The objective is to minimize the travel time of the TC between yard-bays and setup time for the TC in a visiting yard. In this paper, we shows that the problem is NP-complete, and suggests a new formulation for it. Using the new formulation for the problem, we investigate some characteristics of solutions, a lower and upper bounds for it. Moreover, our lower and upper bound is very efficient to applying some instances suggested in a previous work.

• Journal of information and communication convergence engineering
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• v.15 no.1
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• pp.21-27
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• 2017

In this research, we study the outage probability for distributed space-time coding-based cooperative (DSTC) systems with amplify-and-forward relaying over Rayleigh fading channels with a high temporal correlation where the direct link between the source and the destination is available. In particular, we derive the upper and lower bounds of the outage probability as well as their corresponding asymptotic expressions. In addition, using only the average channel powers for the source-to-relay and relay-to-destination links, we propose an efficient power allocation scheme between the source and the relay to minimize the asymptotic upper bound of the outage probability. Through a numerical investigation, we verify the analytical expressions as well as the effectiveness of the proposed efficient power allocation. The numerical results show that the lower and upper bounds tightly correspond to the exact outage probability, and the proposed efficient power allocation scheme provides an outage probability similar to that of the optimal power allocation scheme that minimizes the exact outage probability.

• Journal of Communications and Networks
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• v.10 no.2
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• pp.194-203
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• 2008

This paper considers the multi-input multi-output (MIMO) relay channel where multiple antennas are employed by each terminal. Compared to single-input single-output (SISO) relay channels, MIMO relay channels introduce additional degrees of freedom, making the design and analysis of optimal cooperative strategies more complex. In this paper, a partial cooperation strategy that combines transmit-side message splitting and block-Markov encoding is presented. Lower bounds on capacity that improve on a previously proposed non-cooperative lower bound are derived for Gaussian MIMO relay channels.

• Management Science and Financial Engineering
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• v.17 no.2
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• pp.1-21
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• 2011

This paper considers an integrated inventory-distribution system with a fleet of heterogeneous vehicles employed where a single warehouse distributes a single type of products to many spatially distributed retailers to satisfy their dynamic demands. The problem is to determine order planning at the warehouse, and also vehicle schedules and delivery quantities for the retailers with the objective of minimizing the sum of ordering cost at the warehouse, inventory holding cost at both the warehouse and retailers, and transportation cost. For the problem, we give a Mixed Integer Programming formulation and develop a Lagrangean heuristic procedure for computing lower and upper bounds on the optimal solution value. The Lagrangean dual problem of finding the best Lagrangrean lower bound is solved by subgradient optimization. Computational experiments on randomly generated test problems showed that the suggested algorithm gives relatively good solutions in a reasonable amount of computation time.

• Journal of information and communication convergence engineering
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• v.8 no.6
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• pp.721-724
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• 2010

In a network router, packet loss may occur when it overflows due to sudden burst traffic. This paper studies how much large buffers are required to eliminate the packet losses. There are buffers on which packet arrive and one output port to which a packet is transmitted at a time. The buffer management algorithm should determine one of the buffers whose packet is transmitted to the output port at each time. The front packet belonging to the buffer determined by the algorithm is transmitted. The goal is to minimize the sum of the lengths of buffers to transmit all the packets. We provide an optimal off-line algorithm and also we show the lower bounds of on-line algorithms. The on-line algorithm has no prior information of the packets having arrived in the future. Its performance is compared to that of the optimal off-line algorithm.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.169-180
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• 2015

We study the braid indices of the Kanenobu knots. It is known that the Kanenobu knots have the same HOMFLYPT polynomial and the same Khovanov-Rozansky homology. The MFW inequality is known for giving a lower bound of the braid index of a link by applying the HOMFLYPT polynomial. Therefore, it is not easy to determine the braid indices of the Kanenobu knots. In our previous paper, we gave upper bounds and sharper lower bounds of the braid indices of the Kanenobu knots by applying the 2-cable version of the zeroth coefficient HOMFLYPT polynomial. In this paper, we give sharper upper bounds of the braid indices of the Kanenobu knots.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.3
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• pp.855-868
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• 2012

In this paper, we consider the discrete memoryless user relaying channel (DMURC) in which a user-relay switches its operational mode symbol-by-symbol. In particular, we obtain upper and lower bounds on the channel capacity for the general DMURC and then show that these the upper and lower bounds coincide for degraded DMURC. It is also shown that the capacity of the degraded DMURC can be achieved using two separate codebooks corresponding to the two UR states. While the UR is assumed to switch states symbol-by-symbol, the results in this paper is the same as when the UR switches states packet-by-packet.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.389-392
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• 2004

The column generation process for the set-partitioning model of the vehicle routing problem requires repeated solutions of column generation subproblems which has a combinatorial structure similar to that of the traveling salesman problem. This limits the size of the problem that can be addressed. We introduce a new modeling approach, termed route-splitting, which splits each vehicle route into segments, and results in more tractable subproblems. A lower bounding scheme that yields an updated bound at each iteration of the column generation process is developed. Implementation issues, including a technique of controlling columns in the master problem, are explored. Lower bounds are computed on standard benchmark problems with up to 199 customers.