9 research outputs found
Technology diffusion in communication networks
The deployment of new technologies in the Internet is notoriously difficult, as evidence by the myriad of well-developed networking technologies that still have not seen widespread adoption (e.g., secure routing, IPv6, etc.) A key hurdle is the fact that the Internet lacks a centralized authority that can mandate the deployment of a new technology. Instead, the Internet consists of thousands of nodes, each controlled by an autonomous, profit-seeking firm, that will deploy a new networking technology only if it obtains sufficient local utility by doing so. For the technologies we study here, local utility depends on the set of nodes that can be reached by traversing paths consisting only of nodes that have already deployed the new technology.
To understand technology diffusion in the Internet, we propose a new model inspired by work on the spread of influence in social networks. Unlike traditional models, where a node's utility depends only its immediate neighbors, in our model, a node can be influenced by the actions of remote nodes. Specifically, we assume node v activates (i.e. deploys the new technology) when it is adjacent to a sufficiently large connected component in the subgraph induced by the set of active nodes; namely, of size exceeding node v's threshold value \theta(v). We are interested in the problem of choosing the right seedset of nodes to activate initially, so that the rest of the nodes in the network have sufficient local utility to follow suit.
We take the graph and thresholds values as input to our problem. We show that our problem is both NP-hard and does not admit an (1-o(1) ln|V| approximation on general graphs. Then, we restrict our study to technology diffusion problems where (a) maximum distance between any pair of nodes in the graph is r, and (b) there are at most \ell possible threshold values. Our set of restrictions is quite natural, given that (a) the Internet graph has constant diameter, and (b) the fact that limiting the granularity of the threshold values makes sense given the difficulty in obtaining empirical data that parameterizes deployment costs and benefits.
We present algorithm that obtains a solution with guaranteed approximation rate of O(r^2 \ell \log|V|) which is asymptotically optimal, given our hardness results. Our approximation algorithm is a linear-programming relaxation of an 0-1 integer program along with a novel randomized rounding scheme.National Science Foundation (S-1017907, CCF-0915922
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Probabilistic Algorithms for Information and Technology Flows in the Networks
This thesis studies several probabilistic algorithms for information and technology flow in the networks. Information flow refers to the circulation of information in social or communication networks for the purpose of disseminating or aggregating knowledge. Technology flow refers to the process in the network in which nodes incrementally adopt a certain type of technological product such as networking protocols. In this thesis, we study the following problems. First, we consider the scenario where information flow acts as media to disseminate messages. The information flow here is considered as a mechanism of replicating a piece of information from one node to another in a network with a goal to “broadcast” the knowledge to everyone. Our studies focus on a broadcasting algorithm called the flooding algorithm. We give a tight characterization on the completion time of the flooding algorithm when we make natural stochastic assumptions on the evolution of the network. Second, we consider the problem that information flow acts as a device to aggregate statistics. We interpret information flow here as artifacts produced by algorithmic procedures that serve as statistical estimators for the networks. The goal is to maintain accurate estimators with minimal information flow overhead. We study these two problems: first, we consider the continual count tracking problem in a distributed environment where the input is an aggregate stream originating from distinct sites and the updates are allowed to be non-monotonic. We develop an optimal algorithm in communication cost that can continually track the count for a family of stochastic streams. Second, we study the effectiveness of using random walks to estimate the statistical properties of networks. Specifically, we give the first deviation bounds for random walks over finite state Markov chains based on mixing time properties of the chain. Finally, we study the problem where technology flow acts as a key to unlock innovative technology diffusion. Here, the technology flow shall be interpreted as a way to specify the circumstance, in which a node in the network will decide to adopt a new technology. Our studies focus on finding the most cost effective way to deploy networking protocols such as SecureBGP or IPv6 in the Internet. Our result is a near optimal strategy that leverages the patterns of technology flows to facilitate the new technology deployments.Engineering and Applied Science
Approximate Deadline-Scheduling with Precedence Constraints
We consider the classic problem of scheduling a set of n jobs
non-preemptively on a single machine. Each job j has non-negative processing
time, weight, and deadline, and a feasible schedule needs to be consistent with
chain-like precedence constraints. The goal is to compute a feasible schedule
that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan
[Annals of Disc. Math., 1977] in their seminal work introduced this problem and
showed that it is strongly NP-hard, even when all processing times and weights
are 1. We study the approximability of the problem and our main result is an
O(log k)-approximation algorithm for instances with k distinct job deadlines
Node-Weighted Prize Collecting Steiner Tree and Applications
The Steiner Tree problem has appeared in the Karp's list of the first 21 NP-hard problems and is well known as one of the most fundamental problems in Network Design area. We study the Node-Weighted version of the Prize
Collecting Steiner Tree problem.
In this problem, we are given a simple graph with a cost and penalty value associated with each node. Our
goal is to find a subtree T of the graph minimizing the cost of the
nodes in T plus penalty of the nodes not in T. By a reduction
from set cover problem it can be easily shown that the problem cannot be approximated in polynomial time within factor of (1-o(1))ln n unless NP has quasi-polynomial time algorithms, where n is the number of vertices of the graph.
Moss and Rabani claimed an O(log n)-approximation algorithm for the problem using a Primal-Dual approach in their STOC'01 paper \cite{moss2001}. We show that their algorithm is incorrect by providing a counter example in which there is an O(n) gap between the dual solution constructed by their algorithm and the optimal solution. Further, evidence is given that their algorithm probably does not have a simple fix. We propose a new algorithm which is more involved and
introduces novel ideas in primal dual approach for network design problems. Also, our algorithm is a Lagrangian Multiplier Preserving algorithm and we show how this property can be utilized to design an O(log n)-approximation algorithm for the Node-Weighted Quota Steiner Tree problem
using the Lagrangian Relaxation method.
We also show an application of the Node Weighted Quota Steiner Tree problem in designing algorithm with better approximation factor for
Technology Diffusion problem, a problem proposed by Goldberg and Liu
in \cite{goldberg2012} (SODA 2013). In Technology Diffusion, we are given a graph G and a threshold θ(v) associated with each vertex v and we are seeking a set of initial nodes called the seed set.
Technology Diffusion is a dynamic process defined over time in which each vertex is either active or inactive. The vertices in the seed set
are initially activated and each other vertex v gets activated whenever there are at least θ(v) active nodes connected to
v through other active nodes. The Technology Diffusion problem asks to
find the minimum seed set activating all nodes. Goldberg
and Liu gave an O(rllog n)-approximation algorithm for the problem where
r and l are the diameter of G and the number of distinct threshold values, respectively. We improve the approximation factor
to O(min{r,l}log n) by establishing a close connection between the problem and the Node Weighted Quota Steiner Tree problem