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Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
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Cited by 516 (15 self)
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In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader determination) for groups of discretetime agents. In each case, we introduce a linear/nonlinear consensus protocol and provide convergence analysis for the proposed distributed algorithm. Moreover, we establish a connection between the Fiedler eigenvalue of the information flow in a network (i.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing averageconsensus problems. We introduce disagreement functions that play the role of Lyapunov functions in convergence analysis of consensus protocols. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
Flocking for MultiAgent Dynamic Systems: Algorithms and Theory
, 2006
"... In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in freespace and presence of multiple obstacles are considered. We present three flocking algorithms: two for freeflocking and one for constrained flocking. A compre ..."
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Cited by 182 (2 self)
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In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in freespace and presence of multiple obstacles are considered. We present three flocking algorithms: two for freeflocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of latticeshape objects called αlattices. We use a multispecies framework for construction of collective potentials that consist of flockmembers, or αagents, and virtual agents associated with αagents called β and γagents. We show that migration of flocks can be performed using a peertopeer network of agents, i.e. “flocks need no leaders.” A “universal” definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2D and 3D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.
Models of Random Regular Graphs
 In Surveys in combinatorics
, 1999
"... In a previous paper we showed that a random 4regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random dregular g ..."
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Cited by 157 (33 self)
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In a previous paper we showed that a random 4regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random dregular graph for other d between 5 and 10 inclusive is a.a.s. restricted to a range of two integer values: {3, 4} for d = 5, {4, 5} for d = 7, 8, 9, and {5, 6} for d = 10. The proof uses efficient algorithms which a.a.s. colour these random graphs using the number of colours specified by the upper bound. These algorithms are analysed using the differential equation method, including an analysis of certain systems of differential equations with discontinuous right hand sides. 1
On graph kernels: Hardness results and efficient alternatives
 IN: CONFERENCE ON LEARNING THEORY
, 2003
"... As most ‘realworld’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances tha ..."
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Cited by 141 (6 self)
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As most ‘realworld’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances that are represented by graphs. So far, only very specific graphs such as trees and strings have been considered. This paper investigates kernels on labeled directed graphs with general structure. It is shown that computing a strictly positive definite graph kernel is at least as hard as solving the graph isomorphism problem. It is also shown that computing an inner product in a feature space indexed by all possible graphs, where each feature counts the number of subgraphs isomorphic to that graph, is NPhard. On the other hand, inner products in an alternative feature space, based on walks in the graph, can be computed in polynomial time. Such kernels are defined in this paper.
The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
 Surveys in Combinatorics (Cambridge
, 2005
"... ..."
Joint Congestion Control and Media Access Control Design for Ad Hoc Wireless Networks
 In Proc. IEEE INFOCOM
, 2005
"... Abstract—We present a model for the joint design of congestion control and media access control (MAC) for ad hoc wireless networks. Using contention graph and contention matrix, we formulate resource allocation in the network as a utility maximization problem with constraints that arise from content ..."
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Cited by 92 (4 self)
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Abstract—We present a model for the joint design of congestion control and media access control (MAC) for ad hoc wireless networks. Using contention graph and contention matrix, we formulate resource allocation in the network as a utility maximization problem with constraints that arise from contention for channel access. We present two algorithms that are not only distributed spatially, but more interestingly, they decompose vertically into two protocol layers where TCP and MAC jointly solve the system problem. The first is a primal algorithm where the MAC layer at the links generates congestion (contention) prices based on local aggregate source rates, and TCP sources adjust their rates based on the aggregate prices in their paths. The second is a dual subgradient algorithm where the MAC subalgorithm is implemented through scheduling linklayer flows according to the congestion prices of the links. Global convergence properties of these algorithms are proved. This is a preliminary step towards a systematic approach to jointly design TCP congestion control algorithms and MAC algorithms, not only to improve performance, but more importantly, to make their interaction more transparent.
Distibuted cooperative control of multiple vehicle formations using structural potential functions. The 15th IFAC World Congress
, 2002
"... Abstract: In this paper, we propose a framework for formation stabilization of multiple autonomous vehicles in a distributed fashion. Each vehicle is assumed to have simple dynamics, i.e. a doubleintegrator, with a directed (or an undirected) information flow over the formation graph of the vehicle ..."
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Cited by 75 (8 self)
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Abstract: In this paper, we propose a framework for formation stabilization of multiple autonomous vehicles in a distributed fashion. Each vehicle is assumed to have simple dynamics, i.e. a doubleintegrator, with a directed (or an undirected) information flow over the formation graph of the vehicles. Our goal is to find a distributed control law (with an efficient computational cost) for each vehicle that makes use of limited information regarding the state of other vehicles. Here, the key idea in formation stabilization is the use of natural potential functions obtained from structural constraints of a desired formation in a way that leads to a collisionfree, distributed, and bounded state feedback law for each vehicle.
Deciding FirstOrder Properties of Locally TreeDecomposable Graphs
 In Proc. 26th ICALP
, 1999
"... . We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable cl ..."
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Cited by 74 (12 self)
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. We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable class C of graphs and for each property ' of graphs that is denable in rstorder logic, there is a linear time algorithm deciding whether a given graph G 2 C has property '. 1 Introduction It is an important task in the theory of algorithms to nd feasible instances of otherwise intractable algorithmic problems. A notion that has turned out to be extremely useful in this context is that of treewidth of a graph. 3Colorability, Hamiltonicity, and many other NPcomplete properties of graphs can be decided in linear time when restricted to graphs whose treewidth is bounded by a xed constant (see [Bod97] for a survey). Courcelle [Cou90] proved a metatheorem, which easily implies numer...
Maximum common subgraph isomorphism algorithms for the matching of chemical structures
 Journal of ComputerAided Molecular Design
, 2002
"... Received 03.03.2002; accepted in final form 16.08.2002 ..."
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Cited by 58 (0 self)
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Received 03.03.2002; accepted in final form 16.08.2002