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11
MinimumCost Multicast over Coded Packet Networks
 IEEE TRANS. ON INF. THE
, 2006
"... We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as b ..."
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Cited by 120 (26 self)
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We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomialtime solvable optimization problem, ... and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimumcost multicast. By contrast, establishing minimumcost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.
Achieving MinimumCost Multicast: A Decentralized Approach Based on Network Coding
 IN PROCEEDINGS OF IEEE INFOCOM
, 2005
"... We present decentralized algorithms that compute minimumcost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimumco ..."
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Cited by 93 (13 self)
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We present decentralized algorithms that compute minimumcost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimumcost multicast. Our approach is in sharp contrast to the prevailing approach based on approximation algorithms for the directed Steiner tree problem, which is suboptimal and generally assumes centralized computation with full network knowledge. We also give extensions beyond the basic problem of fixedrate multicast in networks with directed pointtopoint links, and consider the problem of minimumenergy multicast in wireless networks as well as the case of a concave utility function at the sender.
A discriminative matching approach to word alignment
 In Proceedings of HLTEMNLP
, 2005
"... We present a discriminative, largemargin approach to featurebased matching for word alignment. In this framework, pairs of word tokens receive a matching score, which is based on features of that pair, including measures of association between the words, distortion between their positions, similari ..."
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Cited by 90 (7 self)
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We present a discriminative, largemargin approach to featurebased matching for word alignment. In this framework, pairs of word tokens receive a matching score, which is based on features of that pair, including measures of association between the words, distortion between their positions, similarity of the orthographic form, and so on. Even with only 100 labeled training examples and simple features which incorporate counts from a large unlabeled corpus, we achieve AER performance close to IBM Model 4, in much less time. Including Model 4 predictions as features, we achieve a relative AER reduction of 22 % in over intersected Model 4 alignments. 1
Structured prediction, dual extragradient and Bregman projections
 Journal of Machine Learning Research
, 2006
"... We present a simple and scalable algorithm for maximummargin estimation of structured output models, including an important class of Markov networks and combinatorial models. We formulate the estimation problem as a convexconcave saddlepoint problem that allows us to use simple projection methods ..."
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Cited by 47 (2 self)
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We present a simple and scalable algorithm for maximummargin estimation of structured output models, including an important class of Markov networks and combinatorial models. We formulate the estimation problem as a convexconcave saddlepoint problem that allows us to use simple projection methods based on the dual extragradient algorithm (Nesterov, 2003). The projection step can be solved using dynamic programming or combinatorial algorithms for mincost convex flow, depending on the structure of the problem. We show that this approach provides a memoryefficient alternative to formulations based on reductions to a quadratic program (QP). We analyze the convergence of the method and present experiments on two very different structured prediction tasks: 3D image segmentation and word alignment, illustrating the favorable scaling properties of our algorithm. 1 1.
Secondorder cone programming relaxation of sensor network localization
 SIAM J. Optimization
, 2007
"... Abstract. The sensor network localization problem has been much studied. Recently Biswas and Ye proposed a semidefinite programming (SDP) relaxation of this problem which has various nice properties and for which a number of solution methods have been proposed. Here, we study a secondorder cone pro ..."
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Cited by 24 (2 self)
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Abstract. The sensor network localization problem has been much studied. Recently Biswas and Ye proposed a semidefinite programming (SDP) relaxation of this problem which has various nice properties and for which a number of solution methods have been proposed. Here, we study a secondorder cone programming (SOCP) relaxation of this problem, motivated by its simpler structure and its potential to be solved faster than SDP. We show that the SOCP relaxation, though weaker than the SDP relaxation, has nice properties that make it useful as a problem preprocessor. In particular, sensors that are uniquely positioned among interior solutions of the SOCP relaxation are accurate up to the square root of the distance error. Thus, these sensors, which are easily identified, are accurately positioned. In our numerical simulation, the interior solution found can accurately position up to 80–90 % of the sensors. We also propose a smoothing coordinate gradient descent method for finding an interior solution that is faster than an interiorpoint method. Key words. sensor network localization, semidefinite program, secondorder cone program, approximation algorithm, error bound
Flow formulations for the student scheduling problem
 Practice and Theory of Automated Timetabling IV, number 2740 in Lecture Notes in Computer Science
, 2003
"... Abstract. We discuss the student scheduling problem as it generally applies to highschools in NorthAmerica. We show that the problem is NPhard and discuss various variations to its formulation. We focus on multicommodity flow problems because there has recently been much work and a number of int ..."
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Cited by 4 (0 self)
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Abstract. We discuss the student scheduling problem as it generally applies to highschools in NorthAmerica. We show that the problem is NPhard and discuss various variations to its formulation. We focus on multicommodity flow problems because there has recently been much work and a number of interesting results on approximates solutions to such problems.
An ɛrelaxation method for separable convex cost generalized network flow problems
 MATH. PROGRAM., SER. A
, 2000
"... ..."
CONVEX COST NETWORK FLOW PROBLEMS1
, 1996
"... Abstract We consider a generic auction method for the solution of the single commodity, separable convex cost network flow problem. This method provides a unifying framework for the fflrelaxation method and the auction/sequential shortest path algorithm and, as a consequence, we develop a unified c ..."
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Abstract We consider a generic auction method for the solution of the single commodity, separable convex cost network flow problem. This method provides a unifying framework for the fflrelaxation method and the auction/sequential shortest path algorithm and, as a consequence, we develop a unified complexity analysis for the two methods. We also present computational results showing that these methods are much faster than earlier relaxation methods, particularly for illconditioned problems.
Abstract
"... We present a simple and scalable algorithm for largemargin estimation of structured models, including an important class of Markov networks and combinatorial models. The estimation problem can be formulated as a quadratic program (QP) that exploits the problem structure to achieve polynomial number ..."
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We present a simple and scalable algorithm for largemargin estimation of structured models, including an important class of Markov networks and combinatorial models. The estimation problem can be formulated as a quadratic program (QP) that exploits the problem structure to achieve polynomial number of variables and constraints. However, offtheshelf QP solvers scale poorly with problem and training sample size. We recast the formulation as a convexconcave saddle point problem that allows us to use simple projection methods. We show the projection step can be solved using combinatorial algorithms for mincost convex flow. We provide linear convergence guarantees for our method and present experiments on two very different structured prediction tasks: 3D image segmentation and word alignment, illustrating the favorable scaling properties of our algorithm. 1
A Note on Function Inversion for the Algorithm of Bertsekas, Polymenakos, and Tseng for Network Flow Problems with Convex, Separable Costs
, 1998
"... We show that the algorithm of Bertsekas, Polymenakos, and Tseng for mincost flows with convex separable costs can be adapted to deal with the case in which inversion of the cost derivative function is difficult. We provide a bound on the computational difficulty of the problem for this case. Key wo ..."
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We show that the algorithm of Bertsekas, Polymenakos, and Tseng for mincost flows with convex separable costs can be adapted to deal with the case in which inversion of the cost derivative function is difficult. We provide a bound on the computational difficulty of the problem for this case. Key words. network optimization, fflrelaxation, network flows AMS Subject Classification. 90C25 Dept. of Information and Decision Sciences(M/C 294), University of Illinois, 601 S. Morgan, Chicago, IL 60607, hagstrom@uic.edu. 1 1 Introduction Bertsekas, Polymenakos, and Tseng[2] have recently published a method for solving a mincost flow problem with convex, separable costs. Under the assumption that the arc cost functions are convex, closed, proper, and piecewise differentiable[4], they provide an algorithm which attains a feasible set of arc flows and a dual set of prices (node potentials) such that for each arc the price differential is within an additive term ffl of satisfying compleme...