A linear time algorithm for binary tree sequences transformation using left-arm and right-arm rotations

[[abstract]]In this paper, we consider a transformation on binary trees using new types of rotations. Each of the newly proposed rotations is permitted only at nodes on the left-arm or the right-arm of a tree. Consequently, we develop a linear time algorithm with at most n-1 rotations for converting weight sequences between any two binary trees. In particular, from an analysis of aggregate method for a sequence of rotations, each rotation of the proposed algorithm can be performed in a constant amortized time. Next, we show that a specific directed rooted tree called rotation tree can be constructed using one of the new type rotations. As a by-product, a naive algorithm for enumerating weight sequences of binary trees in lexicographic order can be implemented by traversing the rotation tree. (c) 2006 Elsevier B.V. All rights reserved.[[note]]SC

Edit distance for a run-length-encoded string and an uncompressed string

[[abstract]]We propose a new algorithm for computing the edit distance of an uncompressed string against a run-length-encoded string. For an uncompressed string of length n and a compressed string with M runs, the algorithm computes their edit distance in time O(Mn). This result directly implies an O(min{mN, Mn}) time algorithm for strings of lengths m and n with M and N runs, respectively. It improves the previous best known time bound O(mN + Mn). (c) 2007 Elsevier B.V. All rights reserved.[[note]]SC

Geodesic-pancyclic graphs

[[abstract]]A shortest path connecting two vertices u and v is called a u-v geodesic. The distance between u and v in a graph G, denoted by d(G)(u, v), is the number of edges in a u-v geodesic. A graph G with n vertices is panconnected if, for each pair of vertices U, V is an element of V(G) and for each integer k with d(G)(U, v) <= k <= n - 1, there is a path of length k in G that connects u and v. A graph G with n vertices is geodesic-pancyclic if, for each pair of vertices U, V E V(G), every ti-v geodesic lies on every cycle of length k satisfying max{2d(G)(u, v), 3} <= k <= n. In this paper, we study sufficient conditions of geodesic-pancyclic graphs. In particular, we show that most of the known sufficient conditions of panconnected graphs can be applied to geodesic-pancyclic graphs. (c) 2007 Elsevier B.V. All rights reserved.[[note]]SC

A Note on &quot;An improved upper bound on the queuenumber of the hypercube&quot;

[[abstract]]None[[note]]SC

The existence and uniqueness of strong kings in tournaments

[[abstract]]A king x in a tournament T is a player who beats any other player y directly (i.e., x -> y) or indirectly through a third player z (i.e., x -> z and z -> y). For x, y epsilon V(T), let b(x, y) denote the number of third players through which x beats y indirectly. Then, a king x is strong if the following condition is fulfilled: b(x, y) > b(y, x) whenever y -> x. In this paper, a result shows that for a tournament on n players there exist exactly k strong kings, 1 <= k <= n, with the following exceptions: k = n - 1 when n is odd and k = n when n is even. Moreover, we completely determine the uniqueness of tournaments. (c) 2007 Elsevier B.V. All rights reserved.[[note]]SC

Seamless channel transition for slotted generalized fibonacci broadcasting

[[abstract]]Periodic Broadcasting schemes are cost- effective methods of implementation of Near Video on Demand systems. While the schemes enjoy the advantage of reducing the demand on server bandwidth, they suffer from the problem of insensitivity to the popularity of videos. However, the popularity of a video does not remain constant in the real world; it varies with time, social events, and so on. From a service provider's viewpoint, given a set of popular videos and limited server bandwidth, it would be desirable to adjust the bandwidth allocated to each of the videos dynamically and seamlessly according to the level of its hotness. In this paper, we first re-formulate the Generalized Fibonacci Broadcasting as the Fixed-Length Segment- Scheduling problem and name the re-formulated scheme the Slotted Generalized Fibonacci Broadcasting (SGFB). We then propose a seamless channel transition enhancement on top of the SGFB scheme so that the service provider is capable of adjusting the channel allocation policy to make the most benefit out of the available bandwidth. The correctness of SGFB together with its performance analysis will be presented. Furthermore, we shall provide mathematical analysis to demonstrate its channel transition behavior.[[note]]SC

Finding a longest common subsequence between a run-length-encoded string and an uncompressed string

[[abstract]]In this paper, we propose an O(min {mN, Mn}) timealgorithm for finding a longest common subsequence of strings X and Y with lengths M and N, respectively, and run-length-encoded lengths in and n, respectively. We propose a new recursive formula for finding a longest common subsequence of Y and X which is in the run-length-encoded format. That is, Y = y(1)y(2) ... y(N) and X = r(1)(l1) r(2)(l2) ... r(m)(1m), where r(i) is the repeated character of run i and l(i) is the number of its repetitions. There are three cases in the proposed recursive formula in which two cases are for r(i) matching y(j). The third case is for r(i) mismatching y(j). We will look specifically at the prior two cases that r(i) matches y(j). To determine which case will be used when r(i) matches y(j), we have to find a specific value which can be obtained by using another of our proposed recursive formulas. (C) 2007 Elsevier Inc. All rights reserved.[[note]]SC

Parallel construction of optimal independent spanning trees on hypercubes

[[abstract]]The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number of advantages, including the increase of fault-tolerance and bandwidth. Thus, the designs of multiple ISTs on several classes of networks have been widely investigated. Tang et al. [S.-M. Tang, Y.-L. Waug, Y.-H. Leu. Optimal independent spanning trees on hypercubes, Journal of Information Science and Engineering 20 (2004) 143-155] studied the problem of constructing k ISTs on k-dimensional hypercube Q(k), and provided a recursive algorithm for their construction (i.e., for constructing k ISTs of Q(k), it needs to build k - 1 ISTs of Q(k-1) in advance). This kind of construction forbids the possibility that the algorithm could be parallelized. In this paper, based on a simple concept called Hamming distance Latin square. we design a new algorithm for generating k ISTs of Q(k). The newly proposed algorithm relies on a simple rule and is easy to be parallelized. As a result. we show that the ISTs we constructed are optimal in the sense that both the heights and the average path length of trees are minimized. (c) 2006 Elsevier B.V. All rights reserved.[[note]]SC

Reducing the height of independent spanning trees in chordal rings

[[abstract]]This paper is concerned with a particular family of regular 4-connected graphs, called chordal rings. Chordal rings are a variation of ring networks. By adding two extra links (or chords) at each vertex in a ring network, the reliability and fault-tolerance of the network are enhanced. Two spanning trees on a graph are said to be independent if they are rooted at the same vertex, say, r, and for each vertex v not equal r, the two paths from r to v, one path in each tree, are internally disjoint. A set of spanning trees on a given graph is said to be independent if they are pairwise independent. Iwasaki et al. [9] proposed a linear time algorithm for finding four independent spanning trees on a chordal ring. In this paper, we give a new linear time algorithm to generate four independent spanning trees with a reduced height in each tree. Moreover, a complete analysis of our improvements on the heights of independent spanning trees is also provided.[[note]]SC