2040851
Decycling numbers of random regular graphs
The decycling number φ(G) of a graph G is the smallest number of vertices which can be removed from G so that the resultant graph contains no cycles. In this paper, we study the decycling numbers of random regular graphs. For a random cubic graph G of order n, we prove that φ(G) = ⌈n/4 + 1/2⌉ holds asymptotically almost surely. This is the result of executing a greedy algorithm for decycling G making use of a randomly chosen Hamilton cycle. For a general random d-regular graph G of order n, where d ≥ 4, we prove that φ(G)/n can be bounded below and above asymptotically almost surely by certain constants b(d) and B(d), depending solely on d, which are determined by solving, respectively, an algebraic equation and a system of differential equations.
20645165
Harper-type lower bounds and the bandwidths of the compositions of graphs
Abstract We give a general Harper-type lower bound for the bandwidth of a graph which is a common generalization of several known results. As applications we get a lower bound for the bandwidth of the composition of two graphs. By using this we determine the bandwidths of some composition graphs such as ( P r × P s )[ H ], ( P r × C s )[ H ] (2 r ≠ s ), ( C r × C s )[ H ] (6 ⩽ 2 r ⩽ s ), etc., for any graph H . Interestingly, the bandwidths of these graphs have nothing to do with the structure of H in general.
18154847
Dynamic domination in fuzzy causal networks
This paper presents a dynamic domination theory for fuzzy causal networks (FCN). There are three major contributions. First, we propose a new inference procedure based on dominating sets. Second, we introduce the concepts of dynamic and minimal dynamic dominating sets (DDS and MDDS) in an FCN. To reflect changes of dominance with time, we also introduce the concept of a dynamic dominating process (DDP) that has significant implications in many real-world problems. We pay a special attention to the minimal dynamic dominating process (MDDP) and develop rules for generating DDP and MDDP. Third, we investigate dynamic dominating sets with extended feedback, which we call effective dynamic dominating sets (EDDS), and related effective dynamic dominating process (EDDP). This study unveils a very important phenomenon in FCN: At any time t, either an EDDS exists or there is a dramatic change of the states of vertices. In the latter case we also identify the special structure of the sub-FCN induced by active vertices.
14780024
Fuzzy causal networks: general model, inference, and convergence
In this paper, we first propose a general framework for fuzzy causal networks (FCNs). Then, we study the dynamics and convergence of such general FCNs. We prove that any general FCN with constant weight matrix converges to a limit cycle or a static state, or the trajectory of the FCN is not repetitive. We also prove that under certain conditions a discrete state general FCN converges to its limit cycle or static state in O(n) steps, where n is the number of vertices of the FCN. This is in striking contrast with the exponential running time 2/sup n/, which is accepted widely for classic FCNs.
34996713
Polynomial Time Solvability Of The Weighted Ring Arc-Loading Problem With Integer Splitting
In the Weighted Ring Arc-Loading Problem with Integer Splitting, we are given a set of communication requests each associated with a non-negative integer weight. The problem is to find a routing scheme such that the maximum load on arcs of the ring is minimized, subject to that the weight of each request may be split into two integral parts routed in two directions around the ring, where the load of an arc is the sum of parts routed through the arc. A pseudo-polynomial algorithm for this problem is implied by a result in [G. Wilfong and P. Winkler, Ring routing and wavelength translation, Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms, San Fancisco, CA, 1998, 333-341]. By refining the rounding technique developed in the same paper, we prove that the problem can be solved in polynomial time.
8520561
Bounding the bandwidths for graphs
Let G;H be nite graphs with jV(H)j>jV(G)j. The bandwidth of G with respect to H is dened to be BH(G) = minmaxuv2E(G)dH((u);(v)), with the minimum taken over all injections from V(G )t oV(H), where dH(x;y) is the distance in H between two vertices x;y 2 V(H). This number is involved with the VLSI design and optimization, especially when the \host" graph H is a path Pn or a cycle Cn of length n = jV(G)j. In these two cases, BH(G) is known to be the ordinary bandwidth B(G) and the cyclic bandwidth Bc(G), respectively, and the corresponding decision problem is NP-complete. So estimations of B(G), Bc(G) and in general BH(G) are needed, especially in determining the bandwidths of some specic graphs. In this paper, we rst propose a systematic method for obtaining lower bounds for the bandwidth BH(G). By using this method, we then get a number of lower bounds for B(G) and Bc(G )i n terms of some distance- and degree-related parameters. c 2000 Elsevier Science B.V. All rights reserved.
13349007
Greedy Algorithms for Client Assignment in Large-Scale Distributed Virtual Environments
Distributed Virtual Environments (DVEs), such as online games, military simulations, collaborative design, etc., are very popular nowadays. To support large-scale DVEs, a multi-server architecture is usually employed, and the virtual world is partitioned into multiple zones for load distribution. The client assignment problem arises when assigning the participating clients to the servers. Current approaches usually assign clients to servers according to the locations of clients in the virtual world, i.e., clients interacting in the same zone of the virtual world will be assigned to the same server. This approach may degrade the interactivity of DVEs if the network delay from a client to its assigned server is large. In this paper, we formulate the client assignment problem, and propose two algorithms to assign clients to servers in a more efficient way. The proposed algorithms are based on the heuristics developed for the well-known Terminal Assignment problem. Simulation results with the BRITE Internet Topology Generator show that our algorithms are effective in enhancing the interactivity of DVEs.
1466117
Redundancy and Robustness of the AS-level Internet topology and its models
A comparison between the topological properties of the measured Internet topology, at the autonomous system level (AS graph), and the equivalent graphs generated by two different power law topology generators are presented. Only one of the synthetic generators reproduces the tier connectivity of the AS graph.
13207643
Towards Modelling The Internet Topology - The Interactive Growth Model
The Internet topology at the Autonomous Systems level (AS graph) has a power-law degree distribution and a tier structure. In this paper, we introduce the Interactive Growth (IG) model based on the joint growth of new nodes and new links. This simple and dynamic model compares favorable with other Internet power-law topology generators because it not only closely resembles the degree distribution of the AS graph, but also accurately matches the hierarchical structure, which is measured by the recently reported rich-club phenomenon.
728
Analyzing and modelling the AS-level Internet topology
Recently we introduced the rich-club phenomenon as a quantitative metric to characterize the tier structure of the Autonomous Systems level Internet topology (AS graph) and we proposed the Interactive Growth (IG) model, which closely matches the degree distribution and hierarchical structure of the AS graph and compares favourble with other available Internet power-law topology generators. Our research was based on the widely used BGP AS graph obtained from the Oregon BGP routing tables. Researchers argue that Traceroute AS graph, extracted from the traceroute data collected by the CAIDA's active probing tool, Skitter, is more complete and reliable. To be prudent, in this paper we analyze and compare topological structures of Traceroute AS graph and BGP AS graph. Also we compare with two synthetic Internet topologies generated by the IG model and the well-known Barabasi-Albert (BA) model. Result shows that both AS graphs show the rich-club phenomenon and have similar tier structures, which are closely matched by the IG model, however the BA model does not show the rich-club phenomenon at all.
7007263
The rich-club phenomenon in the Internet topology
We show that the Internet topology at the autonomous system (AS) level has a rich-club phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The rich-club is a core tier that we measured using the rich-club connectivity and the node-node link distribution. We obtained this core tier without any heuristic assumption between the ASs. The rich-club phenomenon is a simple qualitative way to differentiate between power law topologies and provides a criterion for new network models. To show this, we compared the measured rich-club of the AS graph with networks obtained using the Baraba/spl acute/si-Albert (BA) scale-free network model, the Fitness BA model and the Inet-3.0 model.