Online Hotlink Assignment Algorithm for Adaptive Websites

1. Online Hotlink Assignment Algorithm for Adaptive Websites Poonam Goyal, Navneet Goyal, Ankit Khandelwal, & S Raja Babu Department Of Computer Science & Information Systems BITS, Pilani, INDIA.

2. Introduction Data on the Internet is increasing at an alarming rate Urgent need for improving the Internet performance to cope up with limited bandwidth One of the methods for improving internet performance Creating adaptive websites Websites that adapt themselves according to access patterns

3. Adaptive Websites Approaches for designing adaptive websites: Web Mining mining web logs and user profiles and restructuring the website[25,22,14,20] Hotlink Assignment adding/distributing hotlinks

4. Hotlinks Shortcuts at or near the home page of a website to popular pages (frequently accessed) which could be a number of levels down in the network of the pages. Hotlinks were proposed by Perkowitz and Etzioni [18]. Allows users to access a desired page with minimum number of clicks faster access to data

5. Modeling a Website A website is a “graph” where pages are nodes & hyperlinks are edges Working with graphs is not easy Simplification: Model a website as a “tree” Bose et al. [3] and Kranakis et al. [12] have modeled a website as a full complete binary tree We have also modeled the website as a full complete binary tree

6. Hotlink Assigment Add links to popular pages at or near the home page Bose et al. [3] and Kranakis et al. [12] have modeled a website as a full complete binary tree and restricted the addition of hotlinks to at most one hotlink per page Bose et. al. [3] have shown that, even for uniform distribution of weights (representative of the frequency with which it is visited), the problem of optimal assignment of hotlinks in a website modeled as arbitrary directed graph is NP-hard

7. Hotlink Assigment How to assign hotlinks? If the click sequence is known in advance, we can easily decide which pages are frequently accessed and we can assign hotlinks optimally We call such an approach as ‘Optimal Offline Approach’ WHAT IF the click sequence is not known in advance? Offline hotlink assignment algorithms [5,10,11] ONLINE HOTLINK ALGORITHMS

8. Online Hotlink Assignment Online algorithms work according to streaming input We propose an online algorithm for hotlink assignment, which enables websites to adaptively change according to the input sequence The system tries to minimize the average number of hits (cost) to reach a required page by adding hotlinks to the most popular pages closer to the home page The proposed online algorithm is capable of obtaining considerable savings on the access costs of websites

9. Online Hotlink Assignment We compare the performance of the proposed online algorithm with that of the optimal offline algorithm using the concept of “competitive analysis” An online algorithm A, is said to be c-competitive if  a cost b>0, such that, for every finite input sequence , costA() ≤ c costOPT() + b,  where costA is the cost of the online algorithm, c is a constant or a function of the problem parameters [2], and costOPT is the cost of the optimal offline hotlink assignment algorithm

10. Online Hotlink Assignment To find c, the competitive ratio, for the proposed algorithm, ‘OHA’ , we have identified an ‘adversary’ An adversary is an input sequence which maximizes c An adversary gives an upper-bound for the competitive ratio

11. Problem Statement We model a website as a rooted directed tree T = (V,E), where V is a collection of web pages connected by a set of E links. Root represents the home page of the website Assumption: All information is stored at the leaves & there is a unique path to a given leaf node Each leaf has a weight representing the frequency (popularity) with which it is visited. Objective: To place a hotlink near the home page for a popular web page Metric: Frequency of access of a node/page

12. Competitive Analysis We claim that the following input sequence is the adversary for the problem: ADV = (vi, vi,…,vi)where vi , i Є (1,2, … nd) is a leaf page and is repeated m (finite) times. For this input sequence, the optimal offline algorithm will place vi at the root as hotlink. Average cost of access for ADV is given by =1, which is the minimum cost for accessing any page. The online algorithm, on the other hand, will place vi at the root after number of accesses

13. Competitive Analysis where Proof given in paper The competitive ratio is given by:

14. Result: Competitive Ratio

15. Worst Case Analysis The input sequence: where piis some permutation of all the nodes i.e., all the pages are sequentially accessed in a particular order is the worst case of the algorithm Upper bound for the average cost for our online algorithm is d This is because the input sequence does not utilize all the available hotlink positions

16. Worst Case Analysis The optimal offline hotlink assignment will occupy all the available hotlink positions. We find that: The lower bound for the is given by d - 1/(n-1)2.

17. Worst Case Analysis Table 1. Ratio between upper bound of costOHA and lower bound of costOPT

18. Result: Adversary Fig. 2. Change in average cost with increase in m

19. Result: Simulated Sequence Fig. 3. Average cost with simulated access sequence

20. Future Work k-hotlinks per page Modeling website as an incomplete tree Modeling website as some kind of graph

21. Q & A

22. Thank You