Publications (16)3.44 Total impact
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ABSTRACT: The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. This paper characterizes clawfree cubic graphs whose 1skeleton graphs of perfect matching polytopes have diameter 1.  [Show abstract] [Hide abstract]
ABSTRACT: If a graph has a unique perfect matching, we call it a UPMgraph. In this paper we study UPMgraphs. It was shown by Kotzig that a connected UPMgraph has a cut edge belonging to its unique perfect matching. We strengthen this result to a further structural characterization. Using the stronger result, we present a characterization of clawfree UPMgraphs, and prove that for any fixed positive integer n, the number of edges of saturated UPMgraphs on 2n vertices form an arithmetic progression from (2n+2)⌊log2(n+1)⌋22+⌊log2(n+1)⌋+n+4 to n2 with common difference 2. For a fixed positive integer n, we determine the number of labelled UPMtrees on 2n vertices. For a bipartite UPMgraph which has maximum number of edges, we determine the number of spanning UPMtrees of it.  [Show abstract] [Hide abstract]
ABSTRACT: Consider an acyclic directed network $G$ with sources $S_1, S_2,..., S_l$ and distinct sinks $R_1, R_2,..., R_l$. For $i=1, 2,..., l$, let $c_i$ denote the mincut between $S_i$ and $R_i$. Then, by Menger's theorem, there exists a group of $c_i$ edgedisjoint paths from $S_i$ to $R_i$, which will be referred to as a group of Menger's paths from $S_i$ to $R_i$ in this paper. Although within the same group they are edgedisjoint, the Menger's paths from different groups may have to merge with each other. It is known that by choosing Menger's paths appropriately, the number of mergings among different groups of Menger's paths is always bounded by a constant, which is independent of the size and the topology of $G$. The tightest such constant for the all the abovementioned networks is denoted by $\mathcal{M}(c_1, c_2,..., c_2)$ when all $S_i$'s are distinct, and by $\mathcal{M}^*(c_1, c_2,..., c_2)$ when all $S_i$'s are in fact identical. It turns out that $\mathcal{M}$ and $\mathcal{M}^*$ are closely related to the network encoding complexity for a variety of networks, such as multicast networks, twoway networks and networks with multiple sessions of unicast. Using this connection, we compute in this paper some exact values and bounds in network encoding complexity using a graph theoretical approach.  [Show abstract] [Hide abstract]
ABSTRACT: Connected dominating set (CDS) has been proposed as the virtual backbone to alleviate the broadcasting storm in wireless sensor network. Most recent research has extensively focused on the construction of connected dominating set. However, the nodes in the CDS need to dominate all its neighbors, and then some nodes cover a large number of neighboring nodes. Therefore, it is desirable to construct a capacitated dominating set, where each node can dominate only a certain number of neighbors. In this paper, we study capacitated dominating set and connected capacitated dominating set, and propose two approximation algorithms with small approximation ratios.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we consider how to collect data from sensors deployed in the Euclidean plane in a timeefficient way. We assume that all sensors could adjust their transmission ranges and aggregate data received from other sensors. We adopt a collisionfree transmission model using proper schedules for data transmission. We study the problem of finding the schedule under which data from all sensors could be transmitted to the data sink in the minimal time. We propose an approximation algorithm for this NPhard problem whose performance ratio is bounded by a constant. This significantly improves the existing approximation algorithm that does not have a constant performance ratio.  [Show abstract] [Hide abstract]
ABSTRACT: Unit disk graphs are the intersection graphs of equal sized disks in the plane, they are widely used as a mathematical model for wireless adhoc networks and some problems in computational geometry. In this paper we first show that Roman dominating set and connected Roman dominating set problems in unit disk graphs are NPcomplete, and then present two approximation algorithms for these problems.  [Show abstract] [Hide abstract]
ABSTRACT: Let G be a simple graph containing a perfect matching. G is said to be bipartite matching extendable (BMextendable) if every matching M whose induced subgraph is a bipartite graph extends to a perfect matching. Extremal graph problems are at the core of graph theory. In this paper, we characterize maximally BMunextendable graphs, maximally BMextendable graphs in the class of complete kpartite graphs with k⩾2. 
Article: Approximation algorithms for minimum broadcast schedule problem in wireless sensor networks
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ABSTRACT: A wireless sensor network usually consists of a large number of sensor nodes deployed in a field. One of the major communication operations is to broadcast a message from one node to the rest of the others. In this paper, we adopt the conflictfree communication model and study how to compute a transmission schedule that determines when and where a node should forward the message so that all nodes could receive the message in minimum time. We give two approximation algorithms for this NPhard problem that have better theoretically guaranteed performances than the existing algorithms. The proposed approach could be applied to some other similar problems. Keywordsbroadcast scheduleapproximation algorithmwireless sensor networkunit disk graph MSC90B18  [Show abstract] [Hide abstract]
ABSTRACT: Minimum mconnected kdominating set problem is as follows: Given a graph G=(V,E) and two natural numbers m and k, find a subset S⊆V of minimal size such that every vertex in V∖S is adjacent to at least k vertices in S and the induced graph of S is mconnected. In this paper we study this problem with unit disc graphs and small m, which is motivated by the design of faulttolerant virtual backbone for wireless sensor networks. We propose two approximation algorithms with constant performance ratios for m≤2. We also discuss how to design approximation algorithms for the problem with arbitrarily large m. 
Article: On minimum
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ABSTRACT: In wireless sensor networks, a virtual backbone has been proposed as the routing infrastructure to alleviate the broadcasting storm problem and perform some other tasks such as area monitoring. Previous work in this area has mainly focused on how to set up a small virtual backbone for high efficiency, which is modelled as the minimum Connected Dominating Set (CDS) problem. In this paper we consider how to establish a small virtual backbone to balance efficiency and fault tolerance. This problem can be formalized as the minimum mconnected ktuple dominating set problem, which is a general version of minimum CDS problem with m=1 and k=1. We propose three centralized algorithms with small approximation ratios for small m and improve the current best results for small k. 
Conference Paper: MinimumLatency Broadcast Scheduling in Wireless Ad Hoc Networks
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ABSTRACT: A wide range of applications for wireless ad hoc networks are timecritical and impose stringent requirement on the communication latency. This paper studies the problem MinimumLatency Broadcast Scheduling (MLBS) in wireless ad hoc networks represented by unitdisk graphs. This problem is NPhard. A trivial lower bound on the minimum broadcast latency is the radius R of the network with respect to the source of the broadcast, which is the maximum distance of all the nodes from the source of the broadcast. The previously bestknown approximation algorithm for MLBS produces a broadcast schedule with latency at most 648 R. In this paper, we present three progressively improved approximation algorithms for MLBS. They produce broadcast schedules with latency at most 24 R 23, 16 R 15, and R + O (log R) respectively.  [Show abstract] [Hide abstract]
ABSTRACT: Given a wired network of processors, and a source node that needs to broadcast a message to all other processors in the network, the minimum broadcast time problem is to find a scheme that accomplishes the broadcast in a minimum number of time rounds under the constraint that at each time round, no processor can forward the received message to more than one of its neighbors in the network. This NPhard problem has been extensively studied in literatures. In this paper we focus on a variant of the minimum broadcast time problem: the minimum multicast time problem in wireless sensor networks under collisionfree data transmission model. The goal of the problem is to multicast a message from the source node to a set of destination nodes in a minimum number of time rounds. This problem remains NPhard even in the Euclidean plane and the current best approximation algorithm has performance ratio of 41. In this paper we propose a new algorithm that has performance ratio of 15. 
Conference Paper: Algorithms for Minimum

Conference Paper: The Roman Domination Problem in Unit Disk Graphs.
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ABSTRACT: Unit disk graphs are the intersection graphs of equal sized disks in the plane, they are widely used as a mathematical model for wireless adhoc networks and some problems in computational geometry. In this paper we first show that the Roman domination problem in unit disk graphs is NPhard, and then present a simple linear time approximation algorithm and a polynomialtime approximation scheme for this problem, respectively.  [Show abstract] [Hide abstract]
ABSTRACT: In wireless sensor networks, virtual backbone has been proposed as the routing infrastructure to alleviate the broadcasting storm problem and perform some other tasks such as area monitoring. Previous work in this area has mainly focused on how to set up a small virtual backbone for high efficiency, which is modelled as the minimum Connected Dominating Set (CDS) problem. In this paper we consider how to establish a small virtual backbone to balance efficiency and fault tolerance. This problem can be formalized as the minimum mconnected kdominating set problem, which is a general version of minimum CDS problem with m = 1 and k = 1. In this paper we will propose some approximation algorithms for this problem that beat the current best performance ratios.
Publication Stats
141  Citations  
3.44  Total Impact Points  
Top Journals
Institutions

20102014

Zhengzhou University
 Department of Mathematics
Cheng, Henan Sheng, China


20072008

The University of Hong Kong
 Department of Computer Science
Hong Kong, Hong Kong 
Chinese Academy of Sciences
 Institute of Applied Mathematics
Peping, Beijing, China


1970

City University of Hong Kong
 Department of Computer Science
Chiulung, Kowloon City, Hong Kong
