Chandrashekhar Nagarajan

Maximizing influence in a competitive social network: a follower's perspective

We consider the problem faced by a company that wants to use viral marketing to introduce a new product into a market where a competing product is already being introduced. We assume that consumers will use only one of the two products and will influence their friends in their decision of which product to use. We propose two models for the spread of influence of competing technologies through a social network and consider the influence maximization problem from the followers perspective. In particular we assume the follower has a fixed budget available that can be used to target a subset of consumers and show that, although it is NP-hard to select the most influential subset to target, it is possible to give an efficient algorithm that is within 63% of optimal. Our computational experiments show that by using knowledge of the social network and the set of consumers targeted by the competitor, the follower may in fact capture a majority of the market by targeting a relatively small set of the right consumers.

Offline and online facility leasing

We study the problem of leasing facilities over time, following the general infrastructure leasing problem framework introduced by Anthony and Gupta [1]. If there are K different lease types, Anthony and Gupta give an O(K)-approximation algorithm for the problem. We are able to improve this to a 3-approximation algorithm by using a variant of the primal-dual facility location algorithm of Jain and Vazirani [5]. We also consider the online version of the facility leasing problem, in which the clients to be served arrive over time and are not known in advance. This problem generalizes both the online facility location problem (introduced by Meyerson [6]) and the parking permit problem (also introduced by Meyerson [7]). We give a deterministic algorithm for the problem that is O(K log n)-competitive. To achieve our result, we modify an O(log n)-competitive algorithm of Fotakis [2] for the online facility location problem.

Approximation Algorithms for Prize-Collecting Network Design Problems with General Connectivity Requirements

In this paper, we introduce the study of prize-collecting network design problems having general connectivity requirements. Prior work considered only 0-1 or very limited connectivity requirements. We introduce general connectivity requirements in the prize-collecting generalized Steiner tree framework of Hajiaghayi and Jain [9], and consider penalty functions linear in the violation of the connectivity requirements. Using Jain’s iterated rounding algorithm [11] as a black box, and ideas from Goemans [7] and Levi, Lodi, Sviridenko [14], we give a 2.54-factor approximation algorithm for the problem. We also generalize the 0-1 requirements of PCF problem introduced by Sharma, Swamy, and Williamson [15] to include general connectivity requirements. Here we assume that the monotone submodular penalty function of Sharma et al. is generalized to a multiset function that can be decomposed into functions in the same form as that of Sharma et al. Using ideas from Goemans and Berstimas [6], we give an (αlogK)-approximation algorithm for the resulting problem, where K is the maximum connectivity requirement, and α= 2.54.