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Improving Load Balance via Resource Exchange in Large-Scale Search Engines

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu

College of Computer Science Nankai University

June 2020

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Background

A simplified architecture of a search engine.

Queries Leaf Machine Answers

...

Broker

[Index Shards]

Leaf Machine Leaf Machine

[Index Shards] [Index Shards]

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Background

Load rebalancing is NP-hard. E.g., Google machine reassignment problem.

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Motivation

Te transient resources affect shard reassignment!

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Motivation

We use the exchangeable machines to facilitate load balancing.

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Shard Reassignment Problem

ML the set of leaf machines ME the set of exchangeable ma- chines M ML ∪ ME R the set of resources S the set of shards cm[r] the capacity of machine m for resource r um[r] the utilization of resource r by machine m utl[r] the expected utilization of re- source r ds[r] the demand for resource r by shard s X Xs,m = 1, shard s is assigned to machine m; Xs,m = 0, oth- erwise Vm if machine m will be returned Te objective function: min

• r∈R
• m∈M

Vm |um[r] − utl[r]| . ,where the um[r] and utl[r] are defined as follows: um[r] =

• s∈S Xs,mds[r]

cm[r] . utl[r] =

• s∈S ds[r]
• m∈ML cm[r].

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Shard Reassignment Problem

Hard constraints:

1

Single principle constraint

2

Capacity constraint

3

Transient constraint

4

Conflict constraint

5

Qota constraint

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SRA overview

Shard Reassignment Algorithm (SRA)

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Te core procedures of SRA in details

Te flowchart:

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Experiment

1 Input setings (synthetic and real ) and baseline (noisy strategy

based local search (NLS), SRA without EX machines)

Table: Summary of the synthetic input setings

C1 C2 C3 C4 C5 C6 C7 C8 r1 range S S L L S S L L r2 range S L S L S L S L machines Homogeneous Heterogeneous the No. shards (α = 0.2) 14074 6281 6285 6121 9358 4572 4651 3882

Table: Summary of the real datasets DS1 to DS4

Instance ID DS1 DS2 DS3 DS4 Machine type Hetero Hetero Hetero Hetero Number of indexes 78 64 123 60 Number of shards 3072 2753 2936 3057 Number of machines 1816 1220 1987 1976 Machine mean Utl. (r1) 0.50 0.74 0.66 0.42 Machine mean Utl. (r2) 0.39 0.66 0.65 0.29

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Experiment

2 Load balancing on synthetic datasets Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Experiment

3 Load balancing on real datasets

DS1 DS2 DS3 DS4 2 4 6 8 10 ·103 2876 1286 5503 3152 1746 1174 5442 1894 1694 1122 5229 1843 Global Imbalance (×103) NLS SRAnoEX SRA

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Experiment

4 Load balancing under different runtimes (unit: minutes) Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Experiment

5 Global imbalance and different

• No. EX. Machines on

synthetic datasets

1 2 3 4 5 6 7 8 9 10 0.5 1 ·103 proportion of exchangeable machines (%) Global Imbalance (×103) C1 C2 C3 C4 C5 C6 C7 C8

6 Global imbalance and different

• No. EX. Machines on real

datasets

1 2 3 4 5 6 7 8 9 10 2 4 6 ·103 proportion of exchangeable machines (%) Global Imbalance (×103) DS1 DS2 DS3 DS4

Kaiyue Duan, Yusen Li, Trent Marbach, Gang Wang, Xiaoguang Liu Improving Load Balance via Resource Exchange in Large-Scale Search Engines

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Experiment

7 Global imbalance under different No. leaf machines

Global Imbalance (×103) 1000 2000 5000 5 10 15 ·103 68% 46% 23% C1 1000 2000 5000 63% 53% 25% C5 NLS SRAnoEX SRA

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Experiment

8 Comparing with the lower bound

C5 C6 C7 C8 1 2 ·102 17% 19% 28% 6% Global Imbalance (×102)

Relaxation NLS SRAnoEX SRA

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Conclusion

Use exchangeable machines and the SRA to handle the shard reassignment problem. Tere are two trade-offs. We have not deploy the SRA on a real search engine.

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