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Buyatbulk network design with protection
 In FOCS ’07: Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
, 2007
"... We consider approximation algorithms for buyatbulk network design, with the additional constraint that demand pairs be protected against a single edge or node failure in the network. In practice, the most popular model used in high speed telecommunication networks for protection against failures, ..."
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We consider approximation algorithms for buyatbulk network design, with the additional constraint that demand pairs be protected against a single edge or node failure in the network. In practice, the most popular model used in high speed telecommunication networks for protection against failures, is the socalled 1+1 model. In this model, two edge or nodedisjoint paths are provisioned for each demand pair. We obtain the first nontrivial approximation algorithms for buyatbulk network design in the 1+1 model for both edge and nodedisjoint protection requirements. Our results are for the singlecable cost model, which is prevalent in optical networks. More specifically, we present a constantfactor approximation for the singlesink case, and an O ( log 3 n) approximation for the multicommodity case. These results are of interest for practical applications and also suggest several new challenging theoretical problems.
Inferring social networks from outbreaks
 In 21st International Conference on Algorithmic Learning Theory (2010
"... Abstract. We consider the problem of inferring the most likely social network given connectivity constraints imposed by observations of outbreaks within the network. Given a set of vertices (or agents) V and constraints (or observations) Si ⊆ V we seek to find a minimum loglikelihood cost (or maximu ..."
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Cited by 5 (2 self)
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Abstract. We consider the problem of inferring the most likely social network given connectivity constraints imposed by observations of outbreaks within the network. Given a set of vertices (or agents) V and constraints (or observations) Si ⊆ V we seek to find a minimum loglikelihood cost (or maximum likelihood) set of edges (or connections) E such that each Si induces a connected subgraph of (V, E). For the offline version of the problem, we prove an Ω(log(n)) hardness of approximation result for uniform cost networks and give an algorithm that almost matches this bound, even for arbitrary costs. Then we consider the online problem, where the constraints are satisfied as they arrive. We give an O(n log(n))competitive algorithm for the arbitrary cost online problem, which has an Ω(n)competitive lower bound. We look at the uniform cost case as well and give an O(n 2/3 log 2/3 (n))competitive algorithm against an oblivious adversary, as well as an Ω ( √ n)competitive lower bound against an adaptive adversary. We examine cases when the underlying network graph is known to be a star or a path, and prove matching upper and lower bounds of Θ(log(n)) on the competitive ratio for them. 1
Approximation Algorithms for Network Design: A Survey
"... In a typical instance of a network design problem, we are given a directed or undirected graph G = (V,E), nonnegative edgecosts ce for all e ∈ E, and our goal is to find a minimumcost subgraph H of G that satisfies some design criteria. For example, we may wish to find a minimumcost set of edges ..."
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In a typical instance of a network design problem, we are given a directed or undirected graph G = (V,E), nonnegative edgecosts ce for all e ∈ E, and our goal is to find a minimumcost subgraph H of G that satisfies some design criteria. For example, we may wish to find a minimumcost set of edges that induces a connected graph (this is the minimumcost spanning tree problem), or we might want to find a minimumcost set of arcs in a directed graph such that every vertex can reach every other vertex (this is the minimumcost strongly connected subgraph problem). This abstract model for network design problems has a large number of practical applications; the design process of telecommunication and traffic networks, and VLSI chip design are just two examples. Many practically relevant instances of network design problems are NPhard, and thus likely intractable. This survey focuses on approximation algorithms as one possible way of circumventing this impasse. Approximation algorithms are efficient (i.e., they run in polynomialtime), and they compute solutions to a given instance of an optimization problem whose objective values are close to those of the respective optimum solutions. More concretely, most of the problems discussed in this survey are minimization problems. We then say that an algorithm is an αapproximation for a given problem if the ratio of the cost of an approximate solution computed by the algorithm to that of an optimum solution is at most α over all instances. In the
Network Construction with Subgraph Connectivity Constraints
"... Abstract. We consider the problem of building a network given connectivity constraints. A network designer is given a set of vertices V and constraints Si ⊆ V, and seeks to build the lowest cost set of edges E such that each Si induces a connected subgraph of (V, E). In the offline version of the pr ..."
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Abstract. We consider the problem of building a network given connectivity constraints. A network designer is given a set of vertices V and constraints Si ⊆ V, and seeks to build the lowest cost set of edges E such that each Si induces a connected subgraph of (V, E). In the offline version of the problem, we prove an Ω(log(n)) hardness of approximation result for unweighted networks (where edge costs are all 1), and give an algorithm that almost matches this bound, even in the weighted case. Then we consider the online problem, where the constraints must be satisfied as they arrive. We give an O(n log(n))competitive algorithm for the weighted online problem, which has an Ω(n) lower bound. We look at the unweighted case as well and give an O(n 2/3 log 2/3 (n))competitive algorithm against an oblivious adversary. We also examine cases when the underlying graph is known to be a star or a path, and prove matching upper and lower bounds of Θ(log n) on the competitive ratio for them. 1
RESEARCH STATEMENT
"... My primary research interest is on the design and analysis of algorithms that can handle uncertainty in the input, especially those in the online and stochastic optimization domains. Since many interesting optimization problems are computationally intractable (NPHard), we resort to designing approx ..."
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My primary research interest is on the design and analysis of algorithms that can handle uncertainty in the input, especially those in the online and stochastic optimization domains. Since many interesting optimization problems are computationally intractable (NPHard), we resort to designing approximation algorithms which provably output good solutions. However, a common assumption in traditional algorithms is that the exact input is known in advance. What if this is not the case? What if there is uncertainty in the input? For instance, the job sizes in a scheduling problem may be revealed only when the job arrives (online optimization). Or the algorithm has some distributional information about each job, but the exact size is revealed only on arrival (stochastic optimization). With the growing size of input data and their typically distributed nature (cloud computing), it has become imperative for algorithms to handle varying forms of input uncertainty. For example, with new markets emerging across the globe, the longterm problem of placing new data centers (and linking them up faulttolerantly) can be cast as an online network design problem. On the other hand, the daytoday task of scheduling requests at these data centers is a stochastic optimization problem, since the algorithm has knowledge of prior request patterns. Unfortunately, current techniques are not robust enough to deal with many of these problems, thus necessitating the need for new algorithmic tools. Answering such questions, and more generally identifying the tools for solving such problems, has been the driving force of much of my research. For example, we designed the first nontrivial
Approximation Algorithms for NETWORK DESIGN AND ORIENTEERING
, 2010
"... This thesis presents approximation algorithms for some N PHard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widelybelieved complexitytheoretic assumption that P ̸ = N P, there are no efficient (i.e., polynomialt ..."
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This thesis presents approximation algorithms for some N PHard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widelybelieved complexitytheoretic assumption that P ̸ = N P, there are no efficient (i.e., polynomialtime) algorithms that solve these problems exactly. Hence, if one desires efficient algorithms for such problems, it is necessary to consider approximate solutions: An approximation algorithm for an N PHard problem is a polynomial time algorithm which, for any instance of the problem, finds a solution whose value is guaranteed to be within a multiplicative factor ρ of the value of an optimal solution to that instance. We attempt to design algorithms for which this factor ρ, referred to as the approximation ratio of the algorithm, is as small as possible. The field of Network Design comprises a large class of problems that deal with constructing networks of low cost and/or high capacity, routing data through existing networks, and many related issues. In this thesis, we focus chiefly on designing faulttolerant networks. Two vertices u, v in a network are said to be kedgeconnected if deleting any set of k − 1 edges leaves u and v connected; similarly, they are kvertex connected if deleting any set of k − 1 other vertices or edges leaves u and v connected. We focus on building networks that are highly connected, meaning
Active Learning of Interaction Networks
, 2009
"... From molecular arrangements to biological organisms, our world is composed of systems of small components interacting with and affecting each other. Scientists often learn the structure of such systems by tampering with them and making observations. In this thesis, we develop methods for automating ..."
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From molecular arrangements to biological organisms, our world is composed of systems of small components interacting with and affecting each other. Scientists often learn the structure of such systems by tampering with them and making observations. In this thesis, we develop methods for automating this process from an active learning perspective, a setting where the learner is not restricted to making passive observations, but can choose to query the data. First, we consider the setting of learning hidden graphs with queries. Each query type is motivated by a realworld problem, from genome sequencing to evolutionary tree reconstruction. We give new algorithms for learning graphs and also consider the problem of verifying the results of the learning task. Next, we turn to value injection queries, which model experiments used to identify gene regulatory networks. We analyze the complexity of learning large alphabet and analog circuits with value injection queries. We then apply this model to social networks, allowing the learner to activate and suppress agents in the network, and we give an optimal algorithm and matching lower bound for this problem. Finally, we examine the passive learner, who watches the output of agents in a social network and must deduce the most likely underlying network. Last, we consider a classical problem in query learning: learning finite automata, which themselves are networks of connected states. We introduce label queries as a generalization of the well studied membership queries. We give algorithms for learning automata using label queries and analyze other models for learning automata.
Noname manuscript No. (will be inserted by the editor) Network Construction with Subgraph Connectivity Constraints
"... the date of receipt and acceptance should be inserted later Abstract We consider the problem introduced by Korach and Stern in [17] of building a network given connectivity constraints. A network designer is given a set of vertices V and constraints Si ⊆ V, and seeks to build the lowest cost set of ..."
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the date of receipt and acceptance should be inserted later Abstract We consider the problem introduced by Korach and Stern in [17] of building a network given connectivity constraints. A network designer is given a set of vertices V and constraints Si ⊆ V, and seeks to build the lowest cost set of edges E such that each Si induces a connected subgraph of (V, E). First, we answer a question posed by Korach and Stern in [18]: for the offline version of the problem, we prove an Ω(log n) hardness of approximation result for uniform cost networks (where edge costs are all 1) and give an algorithm that almost matches this bound, even in the arbitrary cost case. Then we consider the online problem, where the constraints must be satisfied as they arrive. We give an O(n log n)competitive algorithm for the arbitrary cost online problem, which has an Ω(n)competitive lower bound. We look at the uniform cost case as well and give an O(n 2/3 log 2/3 n)competitive algorithm against an oblivious adversary, as well as an Ω ( √ n)competitive lower bound against an adaptive adversary. We also examine cases when the underlying network graph is known to be a star or a path and prove matching upper and lower bounds of Θ(log n) on the competitive ratio for them.
Online Nodeweighted Steiner . . .
"... We obtain the first online algorithms for the nodeweighted Steiner tree, Steiner forest and group Steiner tree problems that achieve a polylogarithmic competitive ratio. Our algorithm for the Steiner tree problem runs in polynomial time, while those for the other two problems take quasipolynomia ..."
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We obtain the first online algorithms for the nodeweighted Steiner tree, Steiner forest and group Steiner tree problems that achieve a polylogarithmic competitive ratio. Our algorithm for the Steiner tree problem runs in polynomial time, while those for the other two problems take quasipolynomial time. Our algorithms can be viewed as online LP rounding algorithms in the framework of Buchbinder and Naor (Foundations and Trends in Theoretical Computer Science, 2009); however, while the natural LP formulation of these problems do lead to fractional algorithms with a polylogarithmic competitive ratio, we are unable to round these LPs online without losing a polynomial factor. Therefore, we design new LP formulations for these problems drawing on a combination of paradigms such as spider decompositions, lowdepth Steiner trees, generalized group Steiner problems, etc. and use the additional structure provided by these to round the more sophisticated LPs losing only a polylogarithmic factor in the competitive ratio. As further applications of our techniques, we also design polynomialtime online algorithms with polylogarithmic competitive ratios for two fundamental network design problems in edgeweighted graphs: the group Steiner forest problem (thereby resolving an open question raised by Chekuri et al (SODA 2008)) and the single source ℓvertex connectivity problem (which complements similar results for the corresponding edgeconnectivity problem due to Gupta et al (STOC 2009)).