35771956
Maximum genus of a graph in terms of its embedding properties
Let G be a graph that is cellularly embedded in the projective plane such that the dual graph is Hamiltonian. Then we prove that G is upper embeddable. In the meantime we also obtain the same result for other general orientable surfaces if the dual graph contains a separating Hamilton circuit.
7153278
Maximum genus and girth of graphs
Abstract In this paper, a lower bound on the maximum genus of a graph in terms of its girth is established as follows: let G be a simple graph with minimum degree at least three, and let g be the girth of G. Then γ(G)⩾ g−2 2(g−1) β(G)+ 1 g−1 except for G=K 4 , where β(G) denotes the cycle rank of G and K4 is the complete graph with four vertices.
8485722
The maximum genus of graphs with diameter three
Abstract This paper shows that if G is a simple graph with diameter three then G is up-embeddable unless G is either a Δ2-graph (Fig. 1) or a Δ3-graph (Fig. 2) with ξ(G) = 2, i.e., the maximum genus γM(G) = (β(G) − 2)/2.
39392055
Maximum genus and chromatic number of graphs
Let T be a spanning tree of a connected graph G. Denote by @x(G,T) the number of components in [email protected]?E(T) with odd number of edges. The value min"[email protected](G,T) is known as the Betti deficiency of G, denoted by @x(G), where the minimum is taken over all spanning trees T of G. It is known (N.H. Xuong, J. Combin. Theory 26 (1979) 217-225) that the maximum genus of a graph is mainly determined by its Betti deficiency @x(G). Let G be a k-edge-connected graph (k=<3) whose complementary graph has the chromatic number m. In this paper we prove that the Betti deficiency @x(G) is bounded by a function f"k(m) on m, and the bound is the best possible. Thus by Xuong's maximum genus theorem we obtain some new results on the lower bounds of the maximum genus of graphs.
8223639
Assignment-based partitioning in a condition monitoring system
A condition monitoring system tracks real-world variables and alerts users when a predefined condition becomes true, e.g., when enemy planes take off, or when suspicious terrorist activities and communication are detected. However, a monitoring server can easily get overwhelmed by rapid incoming data. To prevent this, we partition the condition being monitored and distribute the workload onto several independent servers. In this paper, we study the problem of how to make a partitioned system behave “equivalently” to a one-server system. We identify and formally define three desirable properties of a partitioned system, namely, orderedness, consistency, and completeness. We propose assignment-based partitioning as a solution that can handle opaque conditions and simplifies load balancing. We also look at a few typical partitioned systems, and discuss their merits using several metrics that we define. Finally, an algorithm is presented to reduce complex system configurations to simpler ones.
9264591
Exactly-once semantics in a replicated messaging system
A wide-area distributed message delivery system can use replication to improve performance and availability. However, without safeguards, replicated messages may be delivered to a mobile device more than once, making the device's user repeat actions (e.g. making unnecessary phone calls, firing weapons repeatedly). Alternatively, they may not be delivered at all, making the user miss important messages. In this paper, we address the problem of exactly-once delivery to mobile clients when messages are replicated globally. We define exactly-once semantics and propose algorithms to guarantee it. We also propose and define a relaxed version of exactly-once semantics which is appropriate for limited-capability mobile devices. We study the relative performance of our algorithms compared to the weaker at-least-once semantics, and find that the performance overhead of exactly-once can be minimized in most cases by careful design of the system.
6825460
DynamicWorkflow Management Using Performance Data
An approach to dynamic workflow management and optimisation using performance data is presented. We discuss strategies for choosing an optimal service (based on user specified criteria) from several semantically equivalent Web Services. Such an approach involves finding "similar" services, by first pruning the set of discovered services based on service metadata, and subsequently selecting an optimal service based on data recorded during prior executions of a service and/or current machine loads. We describe the current implementation of the system, and demonstrate this by a BLAST (used in BioInformatics for Protein-alignment) example by using the Ganglia monitoring tool to get performance data.
2495453
A dual index model for contextual information retrieval
In this paper, we propose a dual index model for contextual IR. For each query, we search against both document level and passage level indexes, and use the corresponding merge function to update the weights for both documents and paragraphs by combining the results from both indexes according to the granularity information in metadata. Experiments on 2004 TREC data show that a significant improvement can be made by using the dual index model.
29686713
A note on Ramsey numbers with two parameters
The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices either G contains G1 or G- contains G2, where G- denotes the complement of G. In this paper, some new bounds with two parameters for the Ramsey number R(G1, G2), under some assumptions, are obtained. Especially, we prove that R(K6 - e, K6) ≤ 116 and R(K6 - e, K7) ≤ 202, these improve the two upper bounds for the classical Ramsey number in [S.P. Radziszowski, Small Ramsey number, Electron. J. Combin. DSI (2002) 1-36].