On an overlay network where a number of nodes work autonomously in a decentralized way, the efficiency of broadcasts has a significant impact on the performance of distributed systems built on the network. While a broadcast method using a spanning tree produces a small number of messages, the routing path lengths are prone to be relatively large. Moreover, when multiple nodes can be source nodes, inefficient broadcasts often occur because the efficient tree topology differs for each node. To address this problem, we propose a novel protocol in which a source node selects an efficient tree from multiple spanning trees when broadcasting. Our method shortens routing paths while maintaining a small number of messages. We examined path lengths and the number of messages for broadcasts on various topologies. As a result, especially for a random graph, our proposed method shortened path lengths by approximately 28% compared with a method using a spanning tree, with almost the same number of messages.

Given a graph G=(V, E), where V and E are vertex and edge sets of G, and a subset VNT of vertices called a non-terminal set, a spanning tree with a non-terminal set VNT, denoted by STNT, is a connected and acyclic spanning subgraph of G that contains all vertices of V where each vertex in a non-terminal set is not a leaf. On general graphs, the problem of finding an STNT of G is known to be NP-hard. In this paper, we show that if G is a circular-arc graph then finding an STNT of G is polynomially solvable with respect to the number of vertices.

A set of spanning trees of a graphs G are called completely independent spanning trees (CISTs for short) if for every pair of vertices x, y∈V(G), the paths joining x and y in any two trees have neither vertex nor edge in common, except x and y. Constructing CISTs has applications on interconnection networks such as fault-tolerant routing and secure message transmission. In this paper, we investigate the problem of constructing two CISTs in the balanced hypercube BHn, which is a hypercube-variant network and is superior to hypercube due to having a smaller diameter. As a result, the diameter of CISTs we constructed equals to 9 for BH2 and 6n-2 for BHn when n≥3.

Social networks often demonstrate hierarchical community structure with communities embedded in other ones. Most existing hierarchical community detection methods need one or more tunable parameters to control the resolution levels, and the obtained dendrograms, a tree describing the hierarchical community structure, are extremely complex to understand and analyze. In the paper, we propose a parameter-free hierarchical community detection method based on micro-community and minimum spanning tree. The proposed method first identifies micro-communities based on link strength between adjacent vertices, and then, it constructs minimum spanning tree by successively linking these micro-communities one by one. The hierarchical community structure of social networks can be intuitively revealed from the merging order of these micro-communities. Experimental results on synthetic and real-world networks show that our proposed method exhibits good accuracy and efficiency performance and outperforms other state-of-the-art methods. In addition, our proposed method does not require any pre-defined parameters, and the output dendrogram is simple and meaningful for understanding and analyzing the hierarchical community structure of social networks.

Given a graph G=(V,E), where V and E are vertex and edge sets of G, and a subset VNT of vertices called a non-terminal set, the minimum spanning tree with a non-terminal set VNT, denoted by MSTNT, is a connected and acyclic spanning subgraph of G that contains all vertices of V with the minimum weight where each vertex in a non-terminal set is not a leaf. On general graphs, the problem of finding an MSTNT of G is NP-hard. We show that if G is a series-parallel graph then finding an MSTNT of G is linearly solvable with respect to the number of vertices.

Given a graph G=(V,E) where V and E are a vertex and an edge set, respectively, specified with a subset VNT of vertices called a non-terminal set, the spanning tree with non-terminal set VNT is a connected and acyclic spanning subgraph of G that contains all the vertices of V where each vertex in a non-terminal set is not a leaf. The complexity of finding a spanning tree with non-terminal set VNT on general graphs where each edge has the weight of one is known to be NP-hard. In this paper, we show that if G is an interval graph then finding a spanning tree with a non-terminal set VNT of G is linearly-solvable when each edge has the weight of one.

In this paper, we propose a boundary-aware superpixel segmentation method, which could quickly and exactly extract superpixel with a non-iteration framework. The basic idea is to construct a minimum spanning tree (MST) based on structure edge to measure the local similarity among pixels, and then label each pixel as the index with shortest path seeds. Intuitively, we first construct MST on the original pixels with boundary feature to calculate the similarity of adjacent pixels. Then the geodesic distance between pixels can be exactly obtained based on two-round tree recursions. We determinate pixel label as the shortest path seed index. Experimental results on BSD500 segmentation benchmark demonstrate the proposed method obtains best performance compared with seven state-of-the-art methods. Especially for the low density situation, our method can obtain the boundary-aware oversegmentation region.

Wireless sensor networks usually deploy sensor nodes with limited energy resources in unattended environments so that people have difficulty in replacing or recharging the depleted devices. In order to balance the energy dissipation and prolong the network lifetime, this paper proposes a routing spanning tree-based clustering algorithm (RSTCA) which uses routing spanning tree to analyze clustering. In this study, the proposed scheme consists of three phases: setup phase, cluster head (CH) selection phase and steady phase. In the setup phase, several clusters are formed by adopting the K-means algorithm to balance network load on the basis of geographic location, which solves the randomness problem in traditional distributed clustering algorithm. Meanwhile, a conditional inter-cluster data traffic routing strategy is created to simplify the networks into subsystems. For the CH selection phase, a novel CH selection method, where CH is selected by a probability based on the residual energy of each node and its estimated next-time energy consumption as a function of distance, is formulated for optimizing the energy dissipation among the nodes in the same cluster. In the steady phase, an effective modification that counters the boundary node problem by adjusting the data traffic routing is designed. Additionally, by the simulation, the construction procedure of routing spanning tree (RST) and the effect of the three phases are presented. Finally, a comparison is made between the RSTCA and the current distributed clustering protocols such as LEACH and LEACH-DT. The results show that RSTCA outperforms other protocols in terms of network lifetime, energy dissipation and coverage ratio.

Given a graph G, a set of spanning trees of G are completely independent spanning trees (CISTs for short) if for any vertices x and y, the paths connecting them on these trees have neither vertex nor edge in common, except x and y. Hasunuma (2001, 2002) first introduced the concept of CISTs and conjectured that there are k CISTs in any 2k-connected graph. Later on, this conjecture was unfortunately disproved by Péterfalvi (2012). In this note, we show that Hasunuma's conjecture holds for graphs restricted in the class of 4-regular chordal rings CR(n,d), where both n and d are even integers.

Given a graph G=(V, E), where V and E are vertex and edge sets of G, and a subset VNT of vertices called a non-terminal set, the minimum spanning tree with a non-terminal set VNT, denoted by MSTNT, is a connected and acyclic spanning subgraph of G that contains all vertices of V with the minimum weight where each vertex in a non-terminal set is not a leaf. On general graphs, the problem of finding an MSTNT of G is NP-hard. We show that if G is an outerplanar graph then finding an MSTNT of G is linearly solvable with respect to the number of vertices.

Given a graph G=(V,E) where V and E are a vertex and an edge set, respectively, specified with a subset VNT of vertices called a non-terminal set, the spanning tree with non-terminal set VNT is a connected and acyclic spanning subgraph of G that contains all the vertices of V where each vertex in a non-terminal set is not a leaf. In the case where each edge has the weight of a nonnegative integer, the problem of finding a minimum spanning tree with a non-terminal set VNT of G was known to be NP-hard. However, the complexity of finding a spanning tree on general graphs where each edge has the weight of one was unknown. In this paper, we consider this problem and first show that it is NP-hard even if each edge has the weight of one on general graphs. We also show that if G is a cograph then finding a spanning tree with a non-terminal set VNT of G is linearly solvable when each edge has the weight of one.

The growth of the size of the routing tables limits the scalability of the conventional IP routing. As scalable routing schemes for large-scale networks are highly demanded, this paper proposes and evaluates an efficient geometric routing scheme and related low-cost node design applicable to large-scale networks. The approach guarantees that greedy forwarding on derived coordinates will result in successful packet delivery to every destination in the network by relying on coordinates deduced from a spanning tree of the network. The efficiency of the proposed scheme is measured in terms of routing quality (stretch) and size of the coordinates. The cost of the proposed router is quantified in terms of area complexity of the hardware design and all the evaluations involve comparison with a state-of-the-art approach with virtual coordinates in the hyperbolic plane. Extensive simulations assess the proposal in large topologies consisting of up to 100K nodes. Experiments show that the scheme has stretch properties comparable to geometric routing in the hyperbolic plane, while enabling a more efficient hardware design, and scaling considerably better in terms of storage requirements for coordinate representation. These attractive properties make the scheme promising for routing in large networks.

Two spanning trees T1,T2 of a graph G = (V,E) are independent if they are rooted at the same vertex, say r, and for each vertex v ∈ V, the path from r to v in T1 and the path from r to v in T2 have no common vertices and no common edges except for r and v. In general, spanning trees T1,T2,…,Tk of a graph G = (V,E) are independent if they are pairwise independent. A graph G = (V,E) is called a 2-chordal ring and denoted by CR(N,d1,d2), if V = {0,1,…,N-1} and E = {(u,v)|[v-u]N = 1 or [v-u]N = d1 or [v-u]N = d2, 2 ≤ d1 < d2 ≤ N/2}. CR(N,d1,N/2) is 5-connected if N ≥ 8 is even and d1 ≠ N/2-1. We give an algorithm to construct 5 independent spanning trees of CR(N,d1,N/2),N ≥ 8 is even and 2 ≤ d1 ≤ ⌈N/4⌉.

Let T1,T2,...,Tk be spanning trees in a graph G. If, for any two vertices u,v of G, the paths joining u and v on the k trees are mutually vertex-disjoint, then T1,T2,...,Tk are called completely independent spanning trees (CISTs for short) of G. The construction of CISTs can be applied in fault-tolerant broadcasting and secure message distribution on interconnection networks. Hasunuma (2001) first introduced the concept of CISTs and conjectured that there are k CISTs in any 2k-connected graph. Unfortunately, this conjecture was disproved by Péterfalvi recently. In this note, we give a necessary condition for k-connected k-regular graphs with ⌊k/2⌋ CISTs. Based on this condition, we provide more counterexamples for Hasunuma's conjecture. By contrast, we show that there are two CISTs in 4-regular chordal rings CR(N,d) with N=k(d-1)+j under the condition that k ≥ 4 is even and 0 ≤ j ≤ 4. In particular, the diameter of each constructed CIST is derived.

Robot covering problem has gained attention as having the most promising applications in our real life. Previous spanning tree coverage algorithm addressed this problem well in a static environment, but not in a dynamic one. In this paper, we present and analyze our algorithm workable in a dynamic environment with less shadow areas.

Given a simple connected graph G with n vertices, the spanning tree problem involves finding a tree that connects all the vertices of G. Solutions to this problem have applications in electrical power provision, computer network design, circuit analysis, among others. It is known that highly efficient sequential or parallel algorithms can be developed by restricting classes of graphs. Circular trapezoid graphs are proper superclasses of trapezoid graphs. In this paper, we propose an O(n) time algorithm for the spanning tree problem on a circular trapezoid graph. Moreover, this algorithm can be implemented in O(log n) time with O(n/log n) processors on EREW PRAM computation model.

In this paper, we study the minimum spanning tree problem with label selection, that is, the problem of finding a minimum spanning tree of a vertex-labeled graph where the weight of each edge may vary depending on the selection of labels of vertices at both ends. The problem is especially important as the application to mathematical OCR. It is shown that the problem is NP-hard. However, for the application to mathematical OCR, it is sufficient to deal with only graphs with small tree-width. In this paper, a linear-time algorithm for series-parallel graphs is presented. Since the minimum spanning tree problem with label selection is closely related to the generalized minimum spanning tree problem, their relation is discussed.

In this letter, we propose an improved anchor shot detection (ASD) method in order to effectively retrieve anchor shots from news video. The face location and dissimilarity of icon region are used to reduce false alarms in the proposed method. According to the results of the experiment on several types of news video, the proposed method obtained high anchor detection results compared with previous methods.

Wireless mesh networks have been attracting many users in recent years. By connecting base stations (mesh nodes) with wireless connections, these network can achieve a wide-area wireless environment with flexible configuration and low cost at the risk of radio interference between wireless links. When we utilize wireless mesh networks as infrastructures for Internet access, all network traffic from mobile nodes goes through a gateway node that is directly connected to the wired network. Therefore, it is necessary to distribute the traffic load by deploying multiple gateway nodes. In this paper, we propose a spanning tree construction algorithm for TDMA-based wireless mesh networks with multiple gateway nodes so as to maximize the traffic volume transferred between the mesh network and the Internet (system throughput) by taking account of the traffic load on the gateway nodes, the access link capacity and radio interference. Through a performance evaluation, we show that the proposed algorithm increases the system throughput regardless of the bottleneck position and achieves up to 3.1 times higher system throughput than a conventional algorithm.

We present a recovery scheme based on Self-protected Spanning Tree (SST), which recovers from failure all by itself. In the recovery scheme, the links are assigned birthdays to denote the order in which they are to be considered for adding to the SST. The recovery mechanism, named Birthday-based Link Replacing Mechanism (BLRM), is able to transform a SST into a new spanning tree by replacing some tree links with some non-tree links of the same birthday, which ensures the network connectivity after any single link or node failure. First, we theoretically prove that the SST-based recovery scheme can be applied to arbitrary two-edge connected or two connected networks. Then, the recovery time of BLRM is analyzed and evaluated using Ethernet, and the simulation results demonstrate the effectiveness of BLRM in achieving fast recovery. Also, we point out that BLRM provides a novel load balancing mechanism by fast changing the topology of the SST.