2-连通2-支配集的集中式构造

在无线传感器网络中,通常采用连通支配集来构成一个虚拟骨干网进行分层路由,对重要的目标或环境需要构造容错性高,可靠性好的虚拟骨干网。提出构造网络2-连通2-支配集的两种集中式算法,分别是先回路后支配和先支配后回路。前一种算法是先形成一个由支配点组成的回路,然后以此回路为基础不断地扩充此回路,直到不在回路中的节点为2-被支配为止;后一种算法是首先保证每个非支配点都要变成2-被支配点,然后再使图中所有支配点构成回路。     

Two algorithms for determining a minimum independent dominating set

The problem of determining a minimum independent dominating set is fundamental to both the theory and applications of graphs. Computationally it belongs to the class of hard combinatorial optimization problems known as NP-hard. In this paper, we develop a backtracking algorithm and a dynamic programming algorithm to determine a minimum independent dominating set. Computational experience with the backtracking algorithm on more than 1000 randomly generated graphs ranging from 100 to 200 vertices and from 10% to 60% densities has shown that the algorithm is effective.     

传感器网络中高效的最小连通支配集求解算法

在无线传感器网络中,连通支配集被广泛应用于构建虚拟主干。由于求解最小连通支配集是一个NP难问题,许多近似算法被提出用于构建可用的最小连通支配集。针对当前近似算法存在的不足,我们提出了一个新的分布式近似构造算法—CDS-HG,该算法用层次图对无线传感器网络进行建模,算法用基于竞争的贪心策略从每一层选出最少的节点去支配下一层的所有节点。理论分析和模拟结果表明,CDS-HG算法产生的连通支配集是目前最小,并且其消息复杂度也是目前最低的。     

求解圆盘图中最小连通支配集的近似算法

针对无线传感器网络常用的拓扑模型单位圆盘图,提出了基于分布式贪心策略的近似算法DDT,在算法执行的每一轮中,根据一跳邻域范围内的权值和邻居的状态信息,选举出节点并和已确定的节点连接,逐步构造出网络图中的一个支配树。用概率方法研究了支配树中的节点度的性质,通过对极大独立集和最小连通支配集之间关系的分析,得到单位圆盘图中最小连通支配集问题一个新的近似比。计算结果表明,和相关的分布式算法相比,DDT产生的连通支配集在规模上更优。     

无向图中连通支配集问题的精确算法

图◢G=（V,E）的一个支配集DV是一个顶点子集,使得图中每一个顶点要么在D中,要么至少与D中的一个顶点相连。连通支配集问题是找到一个顶点数最小的支配集S,并且S的导出子图G［S］是连通图。◣该问题是一个经典的NP难问题,可应用于连通设施选址、自适应网络等领域。针对无向图中连通支配集问题,仔细分析该问题的图结构性质,挖掘出若干有效的约简规则和分支规则,设计了一个分支搜索算法,并采用了测量治之方法分析算法的运行时间,最终得到了一个运行时间复杂◢度为O*△（1.93n△）的精确◣算法。     

一种参考能量的最小连通支配集近似算法

在无线传感器网络中,能量效率问题至关重要,构造精简的虚拟骨干网可以节约有限资源,这等同于在图论中求解最小连通支配集(MCDS)问题.由此,提出一种构造MCDS的启发式算法.首先根据均值公式为顶点建立次序表,其次构造极大独立集(MIS),再次连接MIS节点,最后优化.仿真实验表明:该算法能够在短时间内找到规模较小的连通支配集(CDS),并且有效地均衡了各节点能量,延长了网络生命周期.     

A strengthened analysis of a local algorithm for the minimum dominating set problem in planar graphs

In recent years growing interest in local distributed algorithms has widely been observed. This results from their high resistance to errors and damage, as well as from their good performance, which is independent of the size of the network. A local deterministic distributed algorithm finding an approximation of a Minimum Dominating Set in planar graphs has been presented by Lenzen et al., and they proved that the algorithm returns a 130-approximation of the Minimum Dominating Set. In this article we will show that the algorithm is two times more effective than was previously assumed, and we prove that the algorithm by Lenzen et al. outputs a 52-approximation to a Minimum Dominating Set. Therefore the gap between the lower bound and the approximation ratio of the best yet local deterministic distributed algorithm is reduced by half.     

Improved approximation algorithms for minimum AND-circuits problem via k-set cover

Arpe and Manthey [J. Arpe, B. Manthey, Approximability of minimum AND-circuits, Algorithmica 53 (3) (2009) 337-357] recently studied the minimum AND-circuit problem, which is a circuit minimization problem, and showed some results including approximation algorithms, APX-hardness and fixed parameter tractability of the problem. In this note, we show that algorithms via the k-set cover problem yield improved approximation ratios for the minimum AND-circuit problem with maximum degree three. In particular, we obtain an approximation ratio of 1.199 for the problem with maximum degree three and unbounded multiplicity.     

An efficient algorithm for constructing a connected dominating set in mobile ad hoc networks

The connected dominating set (CDS) is widely used as a virtual backbone in mobile ad hoc networks. Although many distributed algorithms for constructing the CDS have been proposed, nearly all of them require two or more separated phases, which may cause problems such as long delay in the later phases when the network size is large. This paper proposes a Distributed Single-Phase algorithm for constructing a connected dominating set, DSP-CDS, in ad hoc networks. The DSP-CDS is an asynchronous distributed algorithm and converges quickly in a single phase. Each node uses one-hop neighborhood information and makes a local decision on whether to join the dominating set. Each node bases its decision on a key variable, strength, which guarantees that the dominating set is connected when the algorithm converges. The rules for computing strength can be changed to accommodate different application needs. The DSP-CDS adapts well to dynamic network topologies, upon which the algorithm makes only necessary local updates to maintain the CDS of the network. The performance of the DSP-CDS can be tuned by adjusting two main parameters. Extensive simulations have demonstrated that those parameters can affect the CDS size, the CDS diameter, and number of rounds for the algorithm to converge. Comparisons with other multiple-phase CDS algorithms have shown that the DSP-CDS converges fast and generates a CDS of comparable size.     

A family of simple distributed minimum connected dominating set-based topology construction algorithms

This paper considers the problem of topology construction to save energy in wireless sensor networks. The proposed topology construction mechanisms build reduced topologies using the Connected Dominating Set approach in a distributed, efficient, and simple manner. This problem is very challenging because the solution must provide a connected network with complete coverage of the area of interest using the minimum number of nodes possible. Further, the algorithms need to be computationally inexpensive and the protocols simple enough in terms of their message and computation complexity, so they do not consume more energy creating the reduced topology than the energy that they are supposed to save. In addition, it is desirable to reduce or completely eliminate the need of localization mechanisms since they introduce additional costs and energy consumption. To this end, we present the family of A3 distributed topology construction algorithms, four simple algorithms that build reduced topologies with very low computational and message complexity without the need of localization information: A3, A3Cov, A3Lite and A3CovLite. The algorithms are compared in sparse and dense networks versus optimal theoretical bounds for connected-coverage topologies and two distributed heuristics found in the literature using the number of active nodes and the ratio of coverage as the main performance metrics. The results demonstrate that there is no clear winner, and rather, trade offs exist. If coverage is not as critical as energy (network lifetime), it would be better to use A3Lite, as it needs fewer number of nodes and messages. If coverage is very important for the application, then the A3CovLite is the best option mostly because of the lower message complexity.     

Efficient parallel algorithms forr-dominating set andp-center problems on trees

We develop efficient parallel algorithms for ther-dominating set and thep-center problems on trees. On a concurrent-read exclusive-write PRAM, our algorithm for ther-dominating set problem runs inO(logn log logn) time withn processors. The algorithm for thep-center problem runs inO(log² n log logn) time withn processors.Xin He was supported in part by an Ohio State University Presidential Fellowship, and by the Office of Research and Graduate Studies of Ohio State University. Yaacov Yesha was supported in part by the National Science Foundation under Grant No. DCR-8606366.     

无线传感器网络中d-Hop 2-连通容错支配集的分布式构造算法

无线传感器网络随节点移动组成自我维持的自组织系统,采用连通支配集的虚拟骨干技术可使平面网络系统层次化而简化节点路由、管理和维护。但大规模无线传感器网络的连通支配集节点数目依然庞大,d-hop连通支配集可以大大减小支配集节点数目。另外,由于存在节点失效、链路断裂等无线特性,虚拟骨干网需要具备一定的容错性。在单位圆盘图网络模型中为构建精简且具有容错能力的虚拟骨干网,提出d-hop 2-连通支配集的分布式构造算法,先构造d-hop独立支配集后再连通形成d-hop 2-连通支配集。并从理论和仿真上对算法的复杂度、近似比和算法性能作了进一步探讨和验证。     

Computing (r, Q) policy for an inventory system with limited sharable resource

This paper deals with inventory systems with limited resource for a single item or multiple items under continuous review (r, Q) policies. For the single-item system with a stochastic demand and limited resource, it is shown that an existing algorithm can be applied to find an optimal (r, Q) policy that minimizes the expected system costs. For the multi-item system with stochastic demands and limited resource commonly shared among all items, an optimization problem is formulated for finding optimal (r, Q) policies for all items, which minimize the expected system costs. Bounds on the parameters (i.e., r and Q) of the optimal policies and bounds on the minimum expected system costs are obtained. Based on the bounds, an algorithm is developed for finding an optimal or near-optimal solution. A method is proposed for evaluating the quality of the solution. It is shown that the algorithm proposed in this paper finds a solution that is (i) optimal/near-optimal and/or (ii) significantly better than the optimal solution with unlimited resource.     

Approximation algorithms for optimization problems in graphs with superlogarithmic treewidth

We present a generic scheme for approximating NP-hard problems on graphs of treewidth k=ω(logn). When a tree-decomposition of width ? is given, the scheme typically yields an ?/logn-approximation factor; otherwise, an extra logk factor is incurred. Our method applies to several basic subgraph and partitioning problems, including the maximum independent set problem.     

A constant approximation algorithm for the densest k-subgraph problem on chordal graphs

The densest k-subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The DkS problem is NP-hard even for special graph classes including bipartite, planar, comparability and chordal graphs, while no constant approximation algorithm is known for any of these classes. In this paper we present a 3-approximation algorithm for the class of chordal graphs. The analysis of our algorithm is based on a graph theoretic lemma of independent interest.     

Generation of random non-overlapping dot patterns for light guides using molecular dynamics simulations with variable r-cut and reflective boundary techniques

This paper presents a molecular dynamics (MD) scheme for the automatic generation of dot patterns for the light guides used in LCD backlight modules. Several MD computational techniques are integrated with the conventional MD scheme to enable the adjustment of the dot density in specific regions of the light guide in order to create a dot distribution with a high dot density variation and a high spatial uniformity. These techniques include the cell division technique, the variable r-cut technique, the boundary smoothing technique and the reflective boundary condition. The reflective boundary condition enables a precise control of the dot density within each cell, and is instrumental in achieving a dot distribution with both a high dot density variation and a high spatial uniformity. The performance of the proposed dot generation scheme is verified by considering the practical example of the dot pattern design of a light guide with a single LED light source located in the lower-right corner. The numerical results confirm the ability of the proposed method to achieve an even luminance condition by establishing a dot pattern whose density increases concentrically with an increasing distance from the light source.     

Distributed algorithms for finding and maintaining a k-tree core in a dynamic network

A k-core C_k of a tree T is subtree with exactly k leaves for k?n_l, where n_l the number of leaves in T, and minimizes the sum of the distances of all nodes from C_k. In this paper first we propose a distributed algorithm for constructing a rooted spanning tree of a dynamic graph such that root of the tree is located near the center of the graph. Then we provide a distributed algorithm for finding k-core of that spanning tree. The spanning tree is constructed in two stages. In the first stage, a forest of trees is generated. In the next stage these trees are connected to form a single rooted tree. An interesting aspect of the first stage of proposed spanning algorithm is that it implicitly constructs the (convex) hull of those nodes which are not already included in the spanning forest. The process is repeated till all non root nodes of the graph have chosen a unique parent. We implemented the algorithms for finding spanning tree and its k-core. A core can be quite useful for routing messages in a dynamic network consisting of a set of mobile devices.     

Clustering in WSN with Latency and Energy Consumption Constraints

  Sensor networks have emerged as a revolutionary technology for querying the physical world and hold promise in a wide variety of applications. However, the extremely energy constrained nature of these networks necessitate that their architecture be designed in an energy-aware manner. Clustering is the architecture of choice as it keeps the traffic local; sensor nodes would send only to nearby cluster-head within a fixed radius, independent of the network size.In this paper we address the problem of clustering in WSNs, subject to upper bounds on the maximum latency, the energy consumed by intermediate nodes, and clusters size. Those constraints are necessary for the reliability of the system and for extending its lifetime. We propose a polynomial time algorithm consisting of recursively computing minimum weighted dominating sets, while respecting latency and energy consumption constraints. We compare our algorithm to other alternatives and show that it consistently outperforms them.

Development of SAW-based multi-gas sensor for simultaneous detection of CO2 and NO2

A 440 MHz wireless and passive surface acoustic wave (SAW)-based multi-gas sensor integrated with a temperature sensor was developed on a 41° YX LiNbO₃ piezoelectric substrate for the simultaneous detection of CO₂, NO₂, and temperature. The developed sensor was composed of a SAW reflective delay lines structured by an interdigital transducer (IDT), ten reflectors, a CO₂ sensitive film (Teflon AF 2400), and a NO₂ sensitive film (indium tin oxide). Teflon AF 2400 was used for the CO₂ sensitive film because it provides a high CO₂ solubility, with good permeability and selectivity. For the NO₂ sensitive film, indium tin oxide (ITO) was used. Coupling of mode (COM) modeling was conducted to determine the optimal device parameters prior to fabrication. Using the parameters determined by the simulation results, the device was fabricated and then wirelessly measured using a network analyzer. The measured reflective coefficient S₁₁ in the time domain showed high signal/noise (S/N) ratio, small signal attenuation, and few spurious peaks. The time positions of the reflection peaks were well matched with the predicted values from the simulation. High sensitivity and selectivity were observed at each target gas testing. The obtained sensitivity was 2.12°/ppm for CO₂ and 51.5°/ppm for NO₂, respectively. With the integrated temperature sensor, temperature compensation was also performed during gas sensitivity evaluation process.