Variable Length-Restricted X-Architecture Steiner Minimum Tree Algorithm Considering Cluster Reduction

LIU Genggeng; LÜ Xingcan; ZHOU Ruping; ZHENG Han; FU Yanggeng

doi:10.12263/DZXB.20260062

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Variable Length-Restricted X-Architecture Steiner Minimum Tree Algorithm Considering Cluster Reduction

PAPERS | 更新时间：2026-06-17

- Variable Length-Restricted X-Architecture Steiner Minimum Tree Algorithm Considering Cluster Reduction
- ACTA ELECTRONICA SINICA Vol. 54, Issue 4, Pages: 1682-1699(2026)
- 作者机构：
  
  1.福州大学计算机与大数据学院，福建福州 350116
  2.大数据智能教育部工程研究中心，福建福州 350116
  3.福建省网络计算与智能信息处理重点实验室，福建福州 350116
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(62372109);Fujian Science Fund for Distinguished Young Scholars(2023J06017)
- DOI：10.12263/DZXB.20260062
  CLC： TP301;
- Received：05 March 2026，
  
  Accepted：08 April 2026，
  
  Published：25 April 2026
- 稿件说明：
移动端阅览
刘耿耿, 吕星灿, 周茹平, 等. 考虑簇减少的可变长度限制X结构Steiner最小树算法[J]. 电子学报, 2026, 54(04): 1682-1699.

LIU Genggeng, LÜ Xingcan, ZHOU Ruping, et al. Variable Length-Restricted X-Architecture Steiner Minimum Tree Algorithm Considering Cluster Reduction[J]. Acta Electronica Sinica, 2026, 54(04): 1682-1699.
刘耿耿, 吕星灿, 周茹平, 等. 考虑簇减少的可变长度限制X结构Steiner最小树算法[J]. 电子学报, 2026, 54(04): 1682-1699. DOI：10.12263/DZXB.20260062

LIU Genggeng, LÜ Xingcan, ZHOU Ruping, et al. Variable Length-Restricted X-Architecture Steiner Minimum Tree Algorithm Considering Cluster Reduction[J]. Acta Electronica Sinica, 2026, 54(04): 1682-1699. DOI：10.12263/DZXB.20260062

摘要

多动态电压（Multiple Dynamic Supply Voltage，MDSV）设计模式通过在芯片中划分不同电压域，使各模块在满足性能与时序要求的前提下采用差异化供电，从而降低整体功耗并提升能效。然而，现有的Steiner最小树（Steiner Minimum Tree，SMT）问题相关工作尚未考虑到MDSV设计模式带来的新约束条件与新优化目标，难以满足MDSV设计模式下的可变长度约束，同时也未考虑引入电压转换器（Level Shifter，LS）带来的额外开销。为此，本文提出了一种考虑簇减少的可变长度限制X结构SMT算法（Variable Length-Restricted X-architecture Steiner Minimum Tree algorithm considering Cluster Reduction， VLRXSMT-CR）。首先，为有效求解MDSV设计模式下SMT这一离散化多目标优化问题，提出了离散化的正向学习算子和变异算子，并引入竞争选择机制与基于拥塞度的外部存档更新机制，实现了LS数量和线长的多目标优化。其次，为避免算法过早陷入局部最优并增强迭代后期的局部搜索能力，以进一步提升解的质量，提出了多样化麻雀比例调整策略。再次，为提高算法更新阶段学习对象的多样性，将分层学习机制引入离散麻雀搜索算法（Sparrow Search Algorithm，SSA）更新过程中。最后，为满足MDSV设计约束并进一步优化布线结构，引入了调整与混合精炼策略，对候选解中违反约束条件的布线边进行调整，同时对候选解中的非最优局部拓扑结构进行优化。与现有方法相比，本文提出的算法在线长指标上取得一定优化的同时，在MDSV设计模式下的关键性能指标（LS）使用数量方面取得了38.60%~51.91%的大幅优化。

Abstract

The multiple dynamic supply voltage (MDSV) design paradigm partitions a chip into multiple voltage domains

enabling modules to operate with differentiated supply voltages while meeting performance and timing requirements

thereby reducing overall power consumption and improving energy efficiency. However

existing studies on the Steiner minimum tree (SMT) problem have not yet taken into account the new constraints and optimization objectives introduced by the MDSV design paradigm. Consequently

these methods are unable to effectively handle variable length restriction under the MDSV environment and fail to account for the additional overhead introduced by level shifters (LSs). To address these issues

this paper proposes a variable length-restricted X-architecture SMT algorithm considering cluster reduction (VLRXSMT-CR). First

in order to effectively solve the discrete multi-objective optimization problem of the SMT under the MDSV design paradigm

discrete forward learning operators and mutation operators are proposed. In addition

a competitive selection mechanism and a congestion-based external archive update mechanism are introduced to achieve multi-objective optimization of the number of LSs and routing wirelength. Second

to avoid premature convergence of the algorithm to local optima and to enhance local search capability in the later stages of iteration

thereby further improving solution quality

a diversified sparrow proportion adjustment strategy is proposed. Then

to improve the diversity of learning targets during the algorithm update stage

a hierarchical learning mechanism is introduced into the update process of the discrete sparrow search algorithm (SSA). Finally

in order to satisfy MDSV design constraints and further optimize routing structures

adjustment and hybrid refinement strategies are introduced to adjust routing edges that violate constraint conditions in candidate solutions

while optimizing non-optimal local topological structures in candidate solutions. Compared with existing methods

the proposed algorithm achieves certain improvements in routing wirelength

while obtaining a significant improvement of 38.60% to 51.91% in the number of LSs

which is a key performance metric under the MDSV design paradigm.

关键词

Keywords

references

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