12795062
Mutually independent hamiltonian paths in star networks
Two hamiltonian paths P1 = 〈u1, u2, . . . , un(G)〉 and P2 = 〈v1, v2, . . . , vn(G)〉 of G from u to v are independent if u = u1 = v1, v = vn(G) = un(G), and vi = ui for every 1 < i < n(G). A set of hamiltonian paths, {P1, P2, . . . , Pk }, of G from u to v are mutually independent if any two different hamiltonian paths are independent from u to v . A bipartite graph G is hamiltonian laceable if there exists a hamiltonian path joining any two nodes from different partite sets. A bipartite graph is k -mutually independent hamiltonian laceable if there exists k -mutually independent hamiltonian paths between any two nodes from distinct partite sets. The mutually independent hamiltonian laceability of a bipartite graph G, IHPL(G), is the maximum integer k such that G is k -mutually independent hamiltonian laceable. Let Sn denote the n-dimensional star graph. We prove that IHPL(S2) = 1, IHPL(S3) = 0, and IHPL(Sn) = n − 2 if n ≥ 4. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(2), 110–117 2005
3010311
On the spanning w-wide diameter of the star graph
Let u and v be any two distinct nodes of an undirected graph G, which is k -connected. A container C(u, v ) between u and v is a set of internally disjoint paths {P1, P2, . . . , Pw } between u and v where 1 ≤ w ≤ k . The width of C(u, v ) is w and the length of C(u, v ) {written as l [C(u, v )]} is max{l (Pi ) | 1 ≤ i ≤ w }. A w -container C(u, v ) is a container with width w . The w -wide distance between u and v , dw (u, v ), is min{l (C(u, v )) | C(u, v ) is a w -container}. A w -container C(u, v ) of the graph G is a w ∗-container if every node of G is incident with a path in C(u, v ). That means that the w -container C(u, v ) spans the whole graph. Let Sn be the n-dimensional star graph with n ≥ 5. It is known that Sn is bipartite. In this article, we show that, for any pair of distinct nodes u and v in different partite sets of Sn , there exists an (n − 1)∗-container C(u, v ) and the (n − 1)-wide distance d(n−1)(u, v ) is less than or equal to n! n−2 + 1. In addition, we also show the existence of a 2∗-container C(u, v ) and the 2-wide distance d2(u, v ) is bounded above by n! 2 + 1. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 48(4), 235–249 2006
12579085
The super laceability of the hypercubes
A k-container C(u,v) of a graph G is a set of k disjoint paths joining u to v. A k-container C(u, v) is a k*-container if every vertex of G is incident with a path in C(u,v). A bipartite graph G is k*-laceable if there exists a k*-container between any two vertices u, v from different partite set of G. A bipartite graph G with connectivity k is super laceable if it is i*-laceable for all i ≤ k. A bipartite graph G with connectivity k is f-edge fault-tolerant super laceable if G - F is i*-laceable for any 1 ≤ i ≤ k-f and for any edge subset F with |F|=f r is super laceable. Moreover, Q r is f-edge fault-tolerant super laceable for any f ≤ r - 2.
11189498
On the spanning connectivity of graphs
Abstract A k-container C ( u , v ) of G between u and v is a set of k internally disjoint paths between u and v . A k -container C ( u , v ) of G is a k * - container if it contains all vertices of G . A graph G is k * - connected if there exists a k * -container between any two distinct vertices. The spanning connectivity of G , κ * ( G ) , is defined to be the largest integer k such that G is w * -connected for all 1 ⩽ w ⩽ k if G is a 1 * -connected graph. In this paper, we prove that κ * ( G ) ⩾ 2 δ ( G ) - n ( G ) + 2 if ( n ( G ) / 2 ) + 1 ⩽ δ ( G ) ⩽ n ( G ) - 2 . Furthermore, we prove that κ * ( G - T ) ⩾ 2 δ ( G ) - n ( G ) + 2 - | T | if T is a vertex subset with | T | ⩽ 2 δ ( G ) - n ( G ) - 1 .
36777484
A Simple Decomposition Method for Support Vector Machines
The decomposition method is currently one of the major methods for solving support vector machines. An important issue of this method is the selection of working sets. In this paper through the design of decomposition methods for bound-constrained SVM formulations we demonstrate that the working set selection is not a trivial task. Then from the experimental analysis we propose a simple selection of the working set which leads to faster convergences for difficult cases. Numerical experiments on different types of problems are conducted to demonstrate the viability of the proposed method.
33646984
Isomorphic Antidirected Path Decompositions of Complete Symmetric Graphs
20106221
Radius Margin Bounds for Support Vector Machines with the RBF Kernel
An important approach for efficient support vector machine (SVM) model selection is to use differentiable bounds of the leave-one-out (loo) error. Past efforts focused on finding tight bounds of loo (e.g., radius margin bounds, span bounds). However, their practical viability is still not very satisfactory. Duan, Keerthi, and Poo (2003) showed that radius margin bound gives good prediction for L2-SVM, one of the cases we look at. In this letter, through analyses about why this bound performs well for L2-SVM, we show that finding a bound whose minima are in a region with small loo values may be more important than its tightness. Based on this principle, we propose modified radius margin bounds for L1-SVM (the other case) where the original bound is applicable only to the hard-margin case. Our modification for L1-SVM achieves comparable performance to L2-SVM. To study whether L1-or L2-SVM should be used, we analyze other properties, such as their differentiability, number of support vectors, and number of free support vectors. In this aspect, L1-SVM possesses the advantage of having fewer support vectors. Their implementations are also different, so we discuss related issues in detail.
11669518
Error checking with client-driven pointer analysis
This paper presents a new client-driven pointer analysis algorithm that automatically adjusts its precision in response to the needs of client analyses. Using five significant error detection problems as clients, we evaluate our algorithm on 18 real C programs. We compare the accuracy and performance of our algorithm against several commonly used fixed-precision algorithms. We find that the client-driven approach effectively balances cost and precision, often producing results as accurate as fixed-precision algorithms that are many times more costly. Our algorithm works because many client problems only need a small amount of extra precision applied to selected portions of each input program.
40521773
Cycle decompositions of crowns
Abstract For an integer n ⩾3, the crown S n 0 is defined to be the graph with vertex set { x 0 , x 1 ,…, x n −1 , y 0 , y 1 ,…, y n −1 } and edge set {x i y j : 0⩽i,j⩽n−1, i≠j} . In this paper we give some sufficient conditions for the edge decomposition of the crown into isomorphic cycles.