Yue-Li Wang

Reducing the Height of Independent Spanning Trees in Chordal Rings

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 \neq 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. [CHECK END OF SENTENCE] 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.

Independent Spanning Trees on Multidimensional Torus Networks

Two spanning trees rooted at vertex r in a graph G are called independent spanning trees (ISTs) if for each vertex v in G, vner, the paths from vertex v to vertex r in these two trees are internally distinct. If the connectivity of G is k, the IST problem is to construct k ISTs rooted at each vertex. The IST problem has found applications in fault-tolerant broadcasting, but it is still open for general graphs with connectivity greater than four. In this paper, we shall propose a very simple algorithm for solving the IST problem on multidimensional torus networks. In our algorithm, every vertex can determine its parent for a specific independent spanning tree only depending on its own label. Thus, our algorithm can also be implemented in parallel systems or distributed systems very easily.

A memory-efficient and fast Huffman decoding algorithm

Abstract To reduce the memory size and speed up the process of searching for a symbol in a Huffman tree, we propose a memory-efficient array data structure to represent the Huffman tree. Then, we present a fast Huffman decoding algorithm, which takes O(log n) time and uses ⌜ 3n 2 ⌝ + ⌜ n 2 log n ⌝ + 1 memory space, where n is the number of symbols in a Huffman tree.

On the independent spanning trees of recursive circulant graphs G(cdm,d) with d>2

Two spanning trees of a graph G are said to be independent if they are rooted at the same vertex r, and for each vertex v r in G, the two different paths from v to r, one path in each tree, are internally disjoint. A set of spanning trees of G is independent if they are pairwise independent. The construction of multiple independent spanning trees has many applications in network communication. For instance, it is useful for fault-tolerant broadcasting and secure message distribution. A recursive circulant graph G(N,d) has N=cd^m vertices labeled from 0 to N-1, where d>=2, m>=1, and 1=2, where the number of independent spanning trees matches the connectivity of G(cd^m,d).

Feedback vertex sets in star graphs

In a graph G = (V, E), a subset F ⊂ V(G) is a feedback vertex set of G if the subgraph induced by V(G) \ F is acyclic. In this paper, we propose an algorithm for finding a small feedback vertex set of a star graph. Indeed, our algorithm can derive an upper bound to the size of the feedback vertex set for star graphs. Also by applying the properties of regular graphs, a lower bound can easily be achieved for star graphs.

A linear-time algorithm for solving the center problem on weighted cactus graphs

Abstract For a nontrivial graph G(V,E) , the distance d(u,v) between vertices u and v is the length of a shortest path p(u,v) in G if such a path exists. The eccentricity e(u) of a vertex u in a graph is the distance from u to a vertex furthest from u . That is, e(u)= max {d(u,v)∣v∈V} . The radius of a graph G is defined as min {e(u)∣u∈V} . A center of G is a vertex whose eccentricity is equal to the radius. The center problem is to find all centers of a graph. In this paper, we shall study the center problem on weighted cactus graphs, and develop an optimal algorithm.

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

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 fight-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.

Loopless Generation of Non-regular Trees with a Prescribed Branching Sequence1

An ordered tree is called a non-regular tree with a prescribed branching sequence (or non-regular tree for short) if its internal nodes have a prespecified degree sequence in preorder list. We define a concise representation, called right distance sequences to describe such trees. A coding tree helps us to systematically investigate the structural representation of non-regular trees. Consequently, we present a loopless algorithm to generate Gray-codes of non-regular trees using right distance sequences.

CONSTRUCTING MULTIPLE INDEPENDENT SPANNING TREES ON RECURSIVE CIRCULANT GRAPHS G(2 m ,2) ∗

A recursive circulant graph G(N,d) has N = cdm vertices labeled from 0 to N - 1, where d ⩾ 2, m ⩾ 1, and 1 ⩽ c < d, and two vertices x,y ∈ G(N,d) are adjacent if and only if there is an integer k with 0 ⩽ k ⩽ ⌈logd N⌉ - 1 such that x ± dk ≡ y (mod N). With the aid of recursive structure, such class of graphs has many attractive features and was considered as a topology of interconnection networks for computing systems. The design of multiple independent spanning trees (ISTs) has many applications in network communication. For instance, it is useful for fault-tolerant broadcasting and secure message distribution. In the previous work of Yang et al. (2009), we provided a constructing scheme to build k ISTs on G(cdm,d) with d ⩾ 3, where k is the connectivity of G(cdm,d). However, the proposed constructing rules cannot be applied to the case of d = 2. For the integrity of solving the IST problem on recursive circulant graphs, this paper deals with the case of G(2m,2) using a set of different constructing rules. Especially, we show that the heights of ISTs for G(2m,2) are lower than the known optimal construction of hypercubes with the same number of vertices.

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

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).