Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept...
-
Upload
lindsay-reeves -
Category
Documents
-
view
220 -
download
0
description
Transcript of Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept...
![Page 1: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/1.jpg)
Minimum Back-Walk-Free Latency Problem with Multiple Servers
Yaw-Ling Lin (林耀鈴 )Dept Computer Sci. & Info. Management,Providence University, Taichung, Taiwan
![Page 2: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/2.jpg)
Yaw-Ling Lin, Providence, Taiwan 2
Minimum Latency Problem (MLP)
• Starts from s, sending goods to all other nodes.
• Traveling Salesperson Problem (TSP): Server oriented
• MLP: Client oriented• MLP is also known as
repairman problem or traveling repairman problem (TRP) s
![Page 3: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/3.jpg)
Yaw-Ling Lin, Providence, Taiwan 3
MLP: Formal Definition
![Page 4: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/4.jpg)
Yaw-Ling Lin, Providence, Taiwan 4
MLP vs. TSP• TSP: minimizes the salesman’s total time. Server oriented, egoistic.
– No contstant approximation algorithm for general case.– Christofides (1976): 3/2-approximation ratio for metric case; Arora (1992):
metric TSP does not have PTAS unless P=NP.– Arora (1998 JACM): PTAS on Euclidean case.
• MLP: minimizes the customers’ total time. Clients oriented, altruistic.– Alias: deliveryman problem, traveling repairman problem (TRP).– Afrati (1986): MAX-SNP-hard for metric case.– Goeman (1996): 10.78-approximation ratio for metric case (with Garg, 19
96FOCS, technique); 3.59-approximation ratio for trees.– Arora (1999 STOC): quasi-polynomial ( O(nO(log n) ) approximation scheme
for trees and Euclidean space. – Sitters (2002, IPCO): MLP on trees is NP-complete; not known for caterpi
llars.
![Page 5: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/5.jpg)
Yaw-Ling Lin, Providence, Taiwan 5
MBLP: Back-Walk Free
![Page 6: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/6.jpg)
Yaw-Ling Lin, Providence, Taiwan 6
An Example
![Page 7: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/7.jpg)
Yaw-Ling Lin, Providence, Taiwan 7
Our Results
• COCOON2002, Singapore, single server MBLP( given a starting point of G )– Trees : O(n log n ) time– k-path : O(n log k) ; path is O(n) time– DAG : NP-Hard (Reduce from 3-SAT)
• This talk (CMCT2003), multiple servers MBLP– k servers on paths : O(n2) time– k servers on cycles : O(n3/k ) time– k origins on paths and cycles : O(n3 log k ) time
![Page 8: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/8.jpg)
Yaw-Ling Lin, Providence, Taiwan 8
Properties
![Page 9: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/9.jpg)
Yaw-Ling Lin, Providence, Taiwan 9
Properties (contd’)
![Page 10: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/10.jpg)
Yaw-Ling Lin, Providence, Taiwan 10
Properties (contd’)
![Page 11: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/11.jpg)
Yaw-Ling Lin, Providence, Taiwan 11
Properties (contd’)
<4,2,3,8> is right-skew; < 5, 3, 4, 1, 2, 6 > is not.<5> <3,4> <1,2,6> is decreasing right-skew partitioned.
![Page 12: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/12.jpg)
Yaw-Ling Lin, Providence, Taiwan 12
Properties (contd’)
![Page 13: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/13.jpg)
Yaw-Ling Lin, Providence, Taiwan 13
Path-Partition: Example
![Page 14: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/14.jpg)
Yaw-Ling Lin, Providence, Taiwan 14
Algorithm Path-Partition
![Page 15: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/15.jpg)
Yaw-Ling Lin, Providence, Taiwan 15
Main Result: k-MBLP on Paths
1 2 3 … n
n1 n2 nk…
![Page 16: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/16.jpg)
Yaw-Ling Lin, Providence, Taiwan 16
k-MBLP: Recurrence Scheme
1 2 3 … nn1 n2 nk…
one-server
![Page 17: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/17.jpg)
Yaw-Ling Lin, Providence, Taiwan 17
Base Cases Analysis
![Page 18: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/18.jpg)
Yaw-Ling Lin, Providence, Taiwan 18
k-MBLP on Cycles
less than O(n/k) cuts
![Page 19: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/19.jpg)
Yaw-Ling Lin, Providence, Taiwan 19
k-server Origin Problems
![Page 20: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/20.jpg)
Yaw-Ling Lin, Providence, Taiwan 20
k-origins: Recurrence Scheme
![Page 21: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/21.jpg)
Yaw-Ling Lin, Providence, Taiwan 21
k-origins: Complexity Analysis
![Page 22: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/22.jpg)
Yaw-Ling Lin, Providence, Taiwan 22
k-origins on Cycles
![Page 23: Minimum Back-Walk-Free Latency Problem with Multiple Servers Yaw-Ling Lin ( 林耀鈴 ) Dept Computer Sci. & Info. Management, Providence University, Taichung,](https://reader034.fdocuments.net/reader034/viewer/2022052607/5a4d1b3d7f8b9ab05999f50a/html5/thumbnails/23.jpg)
Yaw-Ling Lin, Providence, Taiwan 23
Future Research
• MLP on caterpillars.• The binary encoding in k-origin setting
could be further exploited.• Multiple servers on trees, paths.