Strategy with low redundant computation for reachability query preserving graph compression

doi:10.11772/j.issn.1001-9081.2019091666

Journal of Computer Applications ›› 2020, Vol. 40 ›› Issue (2): 510-517.DOI: 10.11772/j.issn.1001-9081.2019091666

• CCF Bigdata 2019 • Previous Articles Next Articles

Strategy with low redundant computation for reachability query preserving graph compression

Danfeng ZHAO¹, Junchen LIN¹, Wei SONG¹, Jian WANG¹, Dongmei HUANG²()

^1.College of Information，Shanghai Ocean University，Shanghai 201306，China
^2.Shanghai University of Electric Power，Shanghai 200090，China

Received:2019-08-30 Revised:2019-09-29 Accepted:2019-10-09 Online:2019-10-14 Published:2020-02-10
Contact: Dongmei HUANG
About author:ZHAO Danfeng， born in 1982. Ph. D.， lecturer. Her research interests include big data storage， business process management.
LIN Junchen， born in 1994， M. S. candidate. His research interests include graph computation.
SONG Wei， born in 1977. Ph. D.， professor. Her research interests include computer vision， machine learning， data mining.
WANG Jian， born in 1979. Ph. D.， lecturer. Her research interests include marine information technology.
Supported by:
the National Key Research and Development Program of China(2016YFC1401907)

低冗余计算的可达性查询保持图压缩策略

赵丹枫¹, 林俊辰¹, 宋巍¹, 王建¹, 黄冬梅²()

^1.上海海洋大学信息学院，上海 201306
^2.上海电力大学，上海 200090

通讯作者: 黄冬梅
作者简介:赵丹枫（1982—），女，黑龙江五常人，讲师，博士，CCF会员，主要研究方向：大数据存储、业务流程管理
林俊辰（1994—），男，吉林白山人，硕士研究生，主要研究方向：图计算
宋巍（1977—），女，山西大同人，教授，博士，主要研究方向：计算机视觉、机器学习、数据挖掘
王建（1979—），女，湖北武汉人，讲师，博士，主要研究方向：海洋信息技术；
基金资助:
国家重点研发计划项目(2016YFC1401907)

Abstract

Abstract:

Since some computation in reachability Query Preserving Graph Compression （QPGC） algorithm are redundant， a high-performance compression strategy was proposed. In the stage of solving the vertex sets of ancestors and descendants， an algorithm named TSB （Topological Sorting Based algorithm for solving ancestor and descendant sets） was proposed for common graph data. Firstly， the vertices of the graph data were topological sorted. Then， the vertex sets were solved in the order or backward order of the topological sequence， avoiding the redundant computation caused by the ambiguous solution order. And an algorithm based on graph aggregation operation was proposed for graph data with short longest path， namely AGGB （AGGregation Based algorithm for solving ancestor and descendant sets）， so the vertex sets were able to be solved in a certain number of aggregation operations. In the stage of solving reachability equivalence class， a Piecewise Statistical Pruning （PSP） algorithm was proposed. Firstly， piecewise statistics of ancestors and descendants sets were obtained and then the statistics were compared to achieve the coarse matching， and some unnecessary fine matches were pruned off. Experimental results show that compared with QPGC algorithm： in the stage of solving the vertex sets of ancestors and descendants， TSB and AGGB algorithm have the performance averagely increased by 94.22% and 90.00% respectively on different datasets； and in the stage of solving the reachability equivalence class， PSP algorithm has the performance increased by more than 70% on most datasets. With the increasing of the dataset， using TSB and AGGB cooperated with PSP has the performance improved by nearly 28 times. Theoretical analysis and simulation results show that the proposed strategy has less redundant computation and faster compression speed compared to QPGC.

Key words: reachability query, graph compression, query preserving, graph data, topological sorting, aggregation operation

摘要：

针对可达性查询保持图压缩（QPGC）算法存在冗余计算的问题，提出了一种高性能压缩策略。在求解顶点的祖先后代集阶段，针对普通图数据，提出一种基于拓扑排序的求解算法TSB，首先将图数据顶点拓扑排序，然后沿拓扑序列顺序（逆序）求解顶点的祖先（后代）集，避免了求解顺序不明确导致的冗余计算；针对最长路径较短的图数据，提出一种基于图聚合运算的求解算法AGGB，可在确定次数的聚合运算内完成顶点的祖先和后代集的求解。在求解可达性等价类阶段，提出一种分段统计剪枝算法PSP，先对祖先后代集分段统计，再比较统计值以实现粗匹配，剪除了部分不必要的精细匹配。实验结果表明，与QPGC算法相比：在祖先后代集求解阶段，TSB和AGGB在不同数据集上的性能平均提升94.22%和90.00%；在求解可达性等价类阶段，PSP算法在大部分数据集上性能提升超过70%；随着数据集的增大，TSB和AGGB配合PSP算法，性能提升了近28倍。理论分析和模拟实验表明，该策略与QPGC算法相比冗余计算更少、压缩速度更快。

关键词: 可达性查询, 图压缩, 查询保持, 图数据, 拓扑排序, 聚合运算

CLC Number:

TP311.12

Danfeng ZHAO, Junchen LIN, Wei SONG, Jian WANG, Dongmei HUANG. Strategy with low redundant computation for reachability query preserving graph compression[J]. Journal of Computer Applications, 2020, 40(2): 510-517.

赵丹枫, 林俊辰, 宋巍, 王建, 黄冬梅. 低冗余计算的可达性查询保持图压缩策略[J]. 《计算机应用》唯一官方网站, 2020, 40(2): 510-517.

Figures/Tables 14

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数据集	顶点数（\|V\|）	边数（\|E\|）	数据来源文献	在文中的缩写
Youtube_0	3 356	3 615	［36］	Y0
Web-California	6 175	16 150	［37］	WebC
Wiki-Vote	7 115	103 689	［37］	WikiV
Youtube_1	26 845	60 603	［36］	Y1
Cit-HepTh	27 769	352 768	［37］	CHT
Cit-HepPh	34 546	421 534	［37］	CHP

数据集	顶点数（\|V\|）	边数（\|E\|）	数据来源文献	在文中的缩写
Youtube_0	3 356	3 615	［36］	Y0
Web-California	6 175	16 150	［37］	WebC
Wiki-Vote	7 115	103 689	［37］	WikiV
Youtube_1	26 845	60 603	［36］	Y1
Cit-HepTh	27 769	352 768	［37］	CHT
Cit-HepPh	34 546	421 534	［37］	CHP

软、硬件环境	配置
操作系统	Ubuntu Server 18.04
CPU	Intel Xeon Gold 6130 CPU @ 2.10 GHz
内核数	2
内存	256 GB
硬盘	1 TB
Spark	2.4.3
Hadoop	2.7
Python	3.7.0
Worker 个数	4

软、硬件环境	配置
操作系统	Ubuntu Server 18.04
CPU	Intel Xeon Gold 6130 CPU @ 2.10 GHz
内核数	2
内存	256 GB
硬盘	1 TB
Spark	2.4.3
Hadoop	2.7
Python	3.7.0
Worker 个数	4

数据集	顶点数（\|V\|）	边数（\|E\|）	压缩图顶点数（\|Vr\|）	压缩图边数（\|Er\|）	压缩率/%
Y0	3 356	3 615	350	248	8.58
WebC	6 175	16 150	3 802	11 826	70.00
WikiV	7 115	103 689	1 016	2 666	3.32
Y1	26 845	60 603	3 717	7 331	12.63
CHT	27 769	352 768	18 821	127 280	38.39
CHP	34 546	421 534	18 683	109 583	28.12

Strategy with low redundant computation for reachability query preserving graph compression

低冗余计算的可达性查询保持图压缩策略

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Figures/Tables 14

References 37

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Metrics

数据集	运行时间/s			加速比/%
数据集	QPGC	TSB	AGGB	TSB	AGGB
Y0	1.34	0.06	0.05	95.28	96.41
WebC	4.67	0.39	0.54	91.60	88.37
WikiV	24.92	1.95	2.25	92.17	90.98
Y1	74.53	1.20	4.03	98.39	94.60
CHT	309.85	15.40	52.23	95.03	83.14
CHP	705.15	50.41	95.33	92.85	86.48

数据集	中间变量占用的存储空间大小
数据集	QPGC/KB	TSB/KB	AGGB/B
Y0	10.27	21.73	6
WebC	18.01	36.53	6
WikiV	19.85	38.48	6
Y1	79.98	165.83	6
CHT	76.00	144.61	6
CHP	89.24	158.67	6

S	不同数据集的存储空间占用大小/KB
S	Y0	WebC	WikiV	Y1	CHT	CHP
2	2 749.71	9 310.76	12 360.94	175 947.49	188 267.87	291 363.81
50	111.44	373.89	496.81	7 038.96	7 538.86	11 655.92
100	55.73	186.95	250.15	3 526.04	3 769.44	5 836.40
200	27.87	93.48	125.08	1 769.58	1 884.73	2 918.21
500	11.48	39.21	52.13	707.84	759.32	1 180.79
1 000	6.57	21.12	27.81	353.93	379.67	590.40

数据集	压缩过程两阶段总体用时/s
数据集	QPGC	TSB+S100	AGGB+S100
Y0	9.48	3.87	3.86
WebC	500.97	36.17	36.32
WikiV	76.83	9.87	10.16
Y1	10 465.31	2 954.20	2 957.03
CHT	41 377.63	1 469.68	1 506.51
CHP	50 557.20	1 824.11	1 869.03

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