• Title, Summary, Keyword: n${\times}$m assignment problem

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ON THE RANDOM n×n ASSIGNMENT PROBLEM

  • Lee, Sung-Chul;Zhonggen, Su
    • Communications of the Korean Mathematical Society
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    • v.17 no.4
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    • pp.719-729
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    • 2002
  • Consider the random n $\times$ m assignment problem with m $\geq$ $_{i,j}$ Let $u_{i,j}$ be iid uniform random variables on [0, 1] and exponential random variables with mean 1, respectively, and let $U_{n, m}$ and $T_{n, m}$ denote the optimal assignment costs corresponding to $u_{i, j}$ and $t_{i, j}$. In this paper we first give a comparison result about the discrepancy E $T_{n, m}$ -E $U_{n, m}$. Using this comparison result with a known lower bound for Var( $T_{n, m}$) we obtains a lower bound for Var( $U_{n, m}$). Finally, we study the way that E $U_{n, m}$ and E $T_{n, m}$ vary as m does. It turns out that only when m - n is large enough, the cost decreases significantly.tly.

Maximum Kill Selection Algorithm for Weapon Target Assignment (WTA) Problem (무기 목표물 배정 문제의 최대 치사인원 선택 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.19 no.2
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    • pp.221-227
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    • 2019
  • It has long been known that weapon target assignment (WTA) problem is NP-hard. Nonetheless, an exact solution can be found using Brute-Force or branch-and bound method which utilize approximation. Many heuristic algorithms, genetic algorithm particle swarm optimization, etc., have been proposed which provide near-optimal solutions in polynomial time. This paper suggests polynomial time algorithm that can be obtain the optimal solution of WTA problem for the number of total weapons k, the number of weapon types m, and the number of targets n. This algorithm performs k times for O(mn) so the algorithm complexity is O(kmn). The proposed algorithm can be minimize the number of trials than brute-force method and can be obtain the optimal solution.

Polynomial Time Algorithm for Satellite Communications Scheduling Problem with Capacity Constrainted Transponder

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.21 no.6
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    • pp.47-53
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    • 2016
  • This paper deals with the capacity constrained time slot assignment problem(CTSAP) that a satellite switches to traffic between $m{\times}n$ ground stations using on-board $k{\leq}_{min}\{m,n\}$ k-transponders switching modes in SS/TDMA time-division technology. There was no polynomial time algorithm to solve the optimal solution thus this problem classified by NP-hard. This paper suggests a heuristic algorithm with O(mn) time complexity to solve the optimal solution for this problem. Firstly, the proposed algorithm selects maximum packet lengths of $\({mn \atop c}\)$ combination and transmits the cut of minimum packet length in each switching mode(MSMC). In the case of last switching mode with inefficient transmission, we applies a compensation strategy to obtain the minimum number of switching modes and the minimum makespan. The proposed algorithm finds optimal solution in polynomial time for all of the experimental data.

Swap-Insert Algorithm for Driver Scheduling Problem (운전기사 일정계획 문제의 교환-삽입 알고리즘)

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.19 no.11
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    • pp.175-181
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    • 2014
  • This paper suggests O(m) polynomial time heuristic algorithm to obtain the solution for the driver scheduling problem, DSP, that has been classified as NP-complete problem. The proposed algorithm gets the initial assignment of n minimum number of drivers from given m schedules. Nextly, this algorithm gets the minimum total time (TC) using 5 rules of swap and insert for decrease of over times (OT) and idle times (IT). Although this algorithm is a heuristic polynomial time algorithm with O(m) time complexity rules to be find a optimal (or approximate) solution, this algorithm is equal to metaheuristic methods for the 5 experimental data. To conclude, this paper shows the DSP is not NP-complete problem but Polynomial time (P)-problem with polynomial time rules.