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52
Bisimulationbased approximate lifted inference
"... There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the firstorder model is given as input to the system. Here, we describe lifted inference algorithms that determine symmetries and automatically lift the probabilistic m ..."
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Cited by 21 (2 self)
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There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the firstorder model is given as input to the system. Here, we describe lifted inference algorithms that determine symmetries and automatically lift the probabilistic model to speedup inference. In particular, we describe approximate lifted inference techniques that allow the user to trade off inference accuracy for computational efficiency by using a handful of tunable parameters, while keeping the error bounded. Our algorithms are closely related to the graphtheoretic concept of bisimulation. We report experiments on both synthetic and real data to show that in the presence of symmetries, runtimes for inference can be improved significantly, with approximate lifted inference providing orders of magnitude speedup over ground inference.
On hierarchical traffic grooming in WDM networks
 IEEE/ACM Transactions on Networking
, 2008
"... Abstract—The traffic grooming problem is of high practical importance in emerging widearea wavelength division multiplexing (WDM) optical networks, yet it is intractable for any but trivial network topologies. In this work, we present an effective and efficient hierarchical traffic grooming framewo ..."
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Cited by 17 (9 self)
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Abstract—The traffic grooming problem is of high practical importance in emerging widearea wavelength division multiplexing (WDM) optical networks, yet it is intractable for any but trivial network topologies. In this work, we present an effective and efficient hierarchical traffic grooming framework for WDM networks of general topology, with the objective of minimizing the total number of electronic ports. At the first level of hierarchy, we decompose the network into clusters and designate one node in each cluster as the hub for grooming traffic. At the second level, the hubs form another cluster for grooming intercluster traffic. We view each (firstor secondlevel) cluster as a virtual star, and we present an efficient nearoptimal algorithm for determining the logical topology of lightpaths to carry the traffic within each cluster. Routing and wavelength assignment is then performed directly on the underlying physical topology. We demonstrate the effectiveness of our approach by applying it to two networks of realistic size, a 32node, 53link topology and a 47node, 96link network. Comparisons to lower bounds indicate that hierarchical grooming is efficient in its use of the network resources of interest, namely, electronic ports and wavelengths. In addition to scaling to large network sizes, our hierarchical approach also facilitates the control and management of multigranular networks. Index Terms—Hierarchical traffic grooming, Kcenter, optical networks, wavelength division multiplexing (WDM).
T.: Distributed approximation of capacitated dominating sets
 In: Proc. 19th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA
, 2007
"... We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) ∈ N for each node v ∈ V, the CapMDS problem asks for a subset S ⊆ V of minimal cardin ..."
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Cited by 12 (1 self)
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We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) ∈ N for each node v ∈ V, the CapMDS problem asks for a subset S ⊆ V of minimal cardinality, such that every network node not in S is covered by at least one neighbor in S, and every node v ∈ S covers at most cap(v) of its neighbors. We prove that in general graphs and even with uniform capacities, the problem is inherently nonlocal, i.e., every distributed algorithm achieving a nontrivial approximation ratio must have a time complexity that essentially grows linearly with the network diameter. On the other hand, if for some parameter ɛ> 0, capacities can be violated by a factor of 1 + ɛ, CapMDS becomes much more local. Particularly, based on a novel distributed randomized rounding technique, we present a distributed bicriteria algorithm that achieves an O(log ∆)approximation in time O(log 3 n + log(n)/ɛ), where n and ∆ denote the number of nodes and the maximal degree in G, respectively. Finally, we prove that in geometric network graphs typically arising in wireless settings, the uniform problem can be approximated within a constant factor in logarithmic time, whereas the nonuniform problem remains entirely nonlocal.
A Distributed Algorithm to Find kdominating Sets
, 1999
"... We consider a connected undirected graph G(n; m) with n nodes and m edges. A kdominating set D in G is a set of nodes having the property that every node in G is at most k edges away from at least one node in D. ..."
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Cited by 11 (0 self)
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We consider a connected undirected graph G(n; m) with n nodes and m edges. A kdominating set D in G is a set of nodes having the property that every node in G is at most k edges away from at least one node in D.
Data Collection for the Sloan Digital Sky Survey  A NetworkFlow Heuristic
 JOURNAL OF ALGORITHMS
, 1996
"... This paper describes an NPhard combinatorial optimization problem arising in the Sloan ..."
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Cited by 9 (0 self)
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This paper describes an NPhard combinatorial optimization problem arising in the Sloan
Compact Location Problems
 Th. Comp. Sci
, 1996
"... We consider the problem of placing a specified number (p) of facilities on the nodes of a network so as to minimize some measure of the distances between facilities. This type of problem models a number of problems arising in facility location, statistical clustering, pattern recognition, and pro ..."
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Cited by 6 (1 self)
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We consider the problem of placing a specified number (p) of facilities on the nodes of a network so as to minimize some measure of the distances between facilities. This type of problem models a number of problems arising in facility location, statistical clustering, pattern recognition, and processor allocation problems in multiprocessor systems. We consider the problem under three different objectives, namely minimizing the diameter, minimizing the average distance, and minimizing the variance. We observe that in general, the problem is NPhard under any of the objectives. Further, even obtaining a constant factor approximation for any of the objectives is NPhard. We present a general framework for obtaining nearoptimal solutions to the compact location problems for the above measures, when the distances satisfy the triangle inequality. We show that this framework can be extended to the case when there are also node weights. Further, we investigate the complexity and ap...
Broadcast domination algorithms for interval graphs, seriesparallel graphs, and trees
 Congressus Numerantium, 169:55 – 77
, 2004
"... y ..."
Facility Location with Dynamic Distance Functions
"... Facility location problems have always been studied with the assumption that the edge lengths in the network are static and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating in ..."
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Cited by 5 (1 self)
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Facility location problems have always been studied with the assumption that the edge lengths in the network are static and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating information centers. In any case, it is clear that due to traffic congestion the traversal time on links changes with time. Very often, we have some estimates as to how the edge lengths change over time, and our objective is to choose a set of locations (vertices) as centers, such that at every time instant each vertex has a center close to it (clearly, the center close to a vertex may change over time). We also provide approximation algorithms as well as hardness results for the Kcenter problem under this model. This is the first comprehensive study regarding approximation algorithms for facility location for good timeinvariant solutions. 1. Introduction Previous theoretical work on fac...
On the application of kcenter algorithms in hierarchical traffic grooming
 IEEE Workshop on Traffic Grooming
, 2005
"... Abstract — In this paper, we study a clustering technique for the hierarchical traffic grooming approach in WDM mesh networks. The objective is to minimize the cost of electronic ports, as well as the wavelength requirement of the solution. In the hierarchical grooming approach we have presented in ..."
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Cited by 5 (2 self)
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Abstract — In this paper, we study a clustering technique for the hierarchical traffic grooming approach in WDM mesh networks. The objective is to minimize the cost of electronic ports, as well as the wavelength requirement of the solution. In the hierarchical grooming approach we have presented in previous work, the first phase is to partition a large mesh network into clusters of nodes. The clustering phase is very important for the final grooming result. Various clustering approaches have been considered in literature; however, not all are suitable for traffic grooming application because they do not take grooming goals into account. In this work, we select a suitable existing clustering algorithm, developed for the KCenter problem, and study its performance as a clustering algorithm for hierarchical grooming. We then improve the algorithm, adapting it specifically for the traffic grooming problem. Experimental results show that the improved version generally provides better solutions than the original algorithm, on various traffic patterns, for the general topology grooming problem instances. I.
An incremental model for combinatorial minimization
, 2006
"... Traditional optimization algorithms are concerned with static input, static constraints, and attempt to produce static output of optimal value. Recent literature has strayed from this conventional approach to deal with more realistic situations in which the input changes over time. Incremental optim ..."
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Cited by 3 (2 self)
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Traditional optimization algorithms are concerned with static input, static constraints, and attempt to produce static output of optimal value. Recent literature has strayed from this conventional approach to deal with more realistic situations in which the input changes over time. Incremental optimization is a new framework for handling this type of dynamic behavior. We consider a general model for producing incremental versions of traditional covering problems along with several natural incremental metrics. Using this model, we demonstrate how to convert conventional algorithms into incremental algorithms with only a constant factor loss in approximation power. We introduce incremental versions of min cut, edge cover, and (k, r)center and present some hardness results. Lastly, we discuss how the incremental model can help us more fully understand online problems and their corresponding algorithms.