• Title/Summary/Keyword: Time complexity

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Hybrid Flow Shop with Parallel Machines at the First Stage and Dedicated Machines at the Second Stage

  • Yang, Jaehwan
    • Industrial Engineering and Management Systems
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    • v.14 no.1
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    • pp.22-31
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    • 2015
  • In this paper, a two-stage hybrid flow shop problem is considered. Specifically, there exist identical parallel machines at stage 1 and two dedicated machines at stage 2, and the objective of the problem is to minimize makespan. After being processed by any machine at stage 1, a job must be processed by a specific machine at stage 2 depending on the job type, and one type of jobs can have different processing times on each machine. First, we introduce the problem and establish complexity of several variations of the problem. For some special cases, we develop optimal polynomial time solution procedures. Then, we establish some simple lower bounds for the problem. In order to solve this NP-hard problem, three heuristics based on simple rules such as the Johnson's rule and the LPT (Longest Processing Time first) rule are developed. For each of the heuristics, we provide some theoretical analysis and find some worst case bound on relative error. Finally, we empirically evaluate the heuristics.

Multicast Tree to Minimize Maximum Delay in Dynamic Overlay Network

  • Lee Chae-Y.;Baek Jin-Woo
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2006.05a
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    • pp.1609-1615
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    • 2006
  • Overlay multicast technique is an effective way as an alternative to IP multicast. Traditional IP multicast is not widely deployed because of the complexity of IP multicast technology and lack of application. But overlay multicast can be easily deployed by effectively reducing complexity of network routers. Because overlay multicast resides on top of densely connected IP network, In case of multimedia streaming service over overlay multicast tree, real-time data is sensitive to end-to-end delay. Therefore, moderate algorithm's development to this network environment is very important. In this paper, we are interested in minimizing maximum end-to-end delay in overlay multicast tree. The problem is formulated as a degree-bounded minimum delay spanning tree, which is a problem well-known as NP-hard. We develop tabu search heuristic with intensification and diversification strategies. Robust experimental results show that is comparable to the optimal solution and applicable in real time

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A Study on the Optimal Rate Allocation Problem in Overlay Multimedia Multicasting (오버레이 멀티캐스트에서 멀티미디어 스트리밍 서비스를 위한 최적 속도 할당에 관한 연구)

  • Chung, Ji-Bok;Choi, Byung-Cheon;Park, Jong-Dae;Ryu, Ho-Yong
    • Journal of the Korean Operations Research and Management Science Society
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    • v.36 no.2
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    • pp.33-42
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    • 2011
  • Overlay multicasting has received a lot of attention as a core technology for multimedia streaming service. In this paper, we consider the discrete optimal rate allocation problem in multimedia overlay multicasting, which has been proposed by Akbari et al.[2]. The computational complexity of this problem is not known. Thus, we propose a special case which can be solved in polynomial time.

Design of Digital Fingerprinting Scheme for Multi-purchase

  • Choi, Jae-Gwi;Rhee, Kyung-Hyune
    • Journal of Korea Multimedia Society
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    • v.7 no.12
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    • pp.1708-1718
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    • 2004
  • In this paper, we are concerned with a digital fingerprinting scheme for multi-purchase where a buyer wants to buy more than a digital content. If we apply previous schemes to multi-purchase protocol, the number of execution of registration step and decryption key should be increased in proportion to that of digital contents to be purchased in order to keep unlinkability. More worse, most of fingerprinting schemes in the literature are based on either secure multi-party computation or general zero-knowledge proofs with very high computational complexity. These high complexities complicate materialization of fingerprinting protocol more and more. In this paper, we propose a multi-purchase fingerprinting scheme with lower computational complexity. In the proposed scheme, a buyer executes just one-time registration step regardless of the number of contents to be purchased. The number of decryption key is constant and independent of the number of contents to be purchased. We can also reduce the computational costs of buyers by introducing a concept of proxy-based fingerprinting protocol.

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STF-OFDM Transmission Scheme via Preceding in Frequency Domain (주파수 영역에서의 사전 부호화를 이용한 STF-OFDM 전송 기법)

  • 박상순;김한경;백흥기
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.29 no.7C
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    • pp.954-961
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    • 2004
  • In this paper, we propose a STF(Space-Time-Frequency) coded OFDM(Orthogonal Frequency Division Multiplexing) transmission scheme as an attractive solution for high bit rate data transmission in a multipath fading environment. The STF-OFDM transmission scheme that we propose in this paper is a simple transmission cheme for achieving frequency diversity gain with low complexity. Using preceding in frequency domain, we obtain frequency diversity gain and improve the SER performance of conventional ST-OFDM. The preceding scheme proposed in this paper is a very simple method that can be encoded and decoded with low complexity.

One-to-All Broadcasting in Petersen-Torus Networks for SLA and MLA Models

  • Seo, Jung-Hyun;Lee, Hyeong-Ok
    • ETRI Journal
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    • v.31 no.3
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    • pp.327-329
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    • 2009
  • In a network, broadcasting is the dissemination of a message from a source node holding a message to all the remaining nodes through a call. This letter proposes a one-to-all broadcasting algorithm in the Petersen-torus network PT(n, n) for the single-link-available and multiple-link-available models. A PT(n, n) is a regular network whose degree is 4 and number of nodes is $10n^2$, where the Petersen graph is set as a basic module, and the basic module is connected in the form of a torus. A broadcasting algorithm is developed using a divide-and-conquer technique, and the time complexity of the proposed algorithm approximates n+4, the diameter of PT(n, n), which is the lower bound of the time complexity of broadcasting.

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A Parallel Search Algorithm and Its Implementation for Digital k-Winners-Take-All Circuit

  • Yoon, Myungchul
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.15 no.4
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    • pp.477-483
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    • 2015
  • The k-Winners-Take-All (kWTA) is an operation to find the largest k (>1) inputs among N inputs. Parallel search algorithm of kWTA for digital inputs is not invented yet, so most of digital kWTA architectures have O(N) time complexity. A parallel search algorithm for digital kWTA operation and the circuits for its VLSI implementation are presented in this paper. The proposed kWTA architecture can compare all inputs simultaneously in parallel. The time complexity of the new architecture is O(logN), so that it is scalable to a large number of digital data. The high-speed kWTA operation and its O(logN) dependency of the new architecture are verified by simulations. It takes 290 ns in searching for 5 winners among 1024 of 32 bit data, which is more than thousands of times faster than existing digital kWTA circuits, as well as existing analog kWTA circuits.

A Term-based Language for Resource-Constrained Project Scheduling and its Complexity Analysis

  • Kutzner, Arne;Kim, Pok-Son
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.12 no.1
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    • pp.20-28
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    • 2012
  • We define a language $\mathcal{RS}$, a subclass of the scheduling language $\mathcal{RS}V$ (resource constrained project scheduling with variant processes). $\mathcal{RS}$ involves the determination of the starting times for ground activities of a project satisfying precedence and resource constraints, in order to minimize the total project duration. In $\mathcal{RS}$ ground activities and two structural symbols (operators) 'seq' and 'pll' are used to construct activity-terms representing scheduling problems. We consider three different variants for formalizing the $\mathcal{RS}$-scheduling problem, the optimizing variant, the number variant and the decision variant. Using the decision variant we show that the problem $\mathcal{RS}$ is $\mathcal{NP}$-complete. Further we show that the optimizing variant (or number variant) of the $\mathcal{RS}$-problem is computable in polynomial time iff the decision variant is computable in polynomial time.

Sub-Exponential Algorithm for 0/1 Knapsack (0/1 Knapsack에 대한 서브-지수 함수 알고리즘)

  • Rhee, Chung Sei
    • Convergence Security Journal
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    • v.14 no.7
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    • pp.59-64
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    • 2014
  • We investigate $p(n){\cdot}2^{O(\sqrt{n})}$ algorithm for 0/1 knapsack problem where x is the total bit length of a list of sizes of n objects. The algorithm is adaptable of method that achieves a similar complexity for the partition and Subset Sum problem. The method can be applied to other optimization or decision problem based on a list of numerics sizes or weights. 0/1 knapsack problem can be used to solve NP-Complete Problems with pseudo-polynomial time algorithm. We try to apply this technique to bio-informatics problem which has pseudo-polynomial time complexity.

Finite-Horizon Online Transmission Scheduling on an Energy Harvesting Communication Link with a Discrete Set of Rates

  • Bacinoglu, Baran Tan;Uysal-Biyikoglu, Elif
    • Journal of Communications and Networks
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    • v.16 no.3
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    • pp.293-300
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    • 2014
  • As energy harvesting communication systems emerge, there is a need for transmission schemes that dynamically adapt to the energy harvesting process. In this paper, after exhibiting a finite-horizon online throughput-maximizing scheduling problem formulation and the structure of its optimal solution within a dynamic programming formulation, a low complexity online scheduling policy is proposed. The policy exploits the existence of thresholds for choosing rate and power levels as a function of stored energy, harvest state and time until the end of the horizon. The policy, which is based on computing an expected threshold, performs close to optimal on a wide range of example energy harvest patterns. Moreover, it achieves higher throughput values for a given delay, than throughput-optimal online policies developed based on infinite-horizon formulations in recent literature. The solution is extended to include ergodic time-varying (fading) channels, and a corresponding low complexity policy is proposed and evaluated for this case as well.