A joint optimization of data ferry trajectories and communication powers of ground sensors for long-term environmental monitoring

Recently, various hybrid wireless sensor networks which consist of several robotic vehicles and a number of static ground sensors have been investigated. In this kind of system, the main role of the mobile nodes is to deliver the messages produced by the sensor nodes, and naturally their trajectory control becomes a significant issue closely related to the performance of the entire system. Previously, several communication power control strategies such as topology control are investigated to improve energy-efficiency of wireless sensor networks. However, to the best of our knowledge, no communication power control strategy has been investigated in the context of the hybrid wireless sensor networks. This paper introduces a new strategy to utilize the communication power control in multiple data ferry assisted wireless sensor network for long-term environmental monitoring such that the lifetime of the sensor network is maximized. We formally define the problem of our interest and show it is NP-hard. We further prove there exists no approximation algorithm for the problem which can produce a feasible solution for every possible problem instance even though there is a feasible solution. Then, we propose heuristic algorithms along with rigorous theoretical performance analysis for both the single data ferry case and the multiple data ferry case under certain condition.     

Minimum power assignment in wireless ad hoc networks with spanner property

Power assignment for wireless ad hoc networks is to assign a power for each wireless node such that the induced communication graph has some required properties. Recently research efforts have focused on finding the minimum power assignment to guarantee the connectivity or fault-tolerance of the network. In this paper, we study a new problem of finding the power assignment such that the induced communication graph is a spanner for the original communication graph when all nodes have the maximum power. Here, a spanner means that the length of the shortest path in the induced communication graph is at most a constant times of the length of the shortest path in the original communication graph. Polynomial time algorithm is given to minimize the maximum assigned power with spanner property. The algorithm also works for any other property that can be tested in polynomial time and is monotone. We then give a polynomial time approximation method to minimize the total transmission radius of all nodes. Finally, we propose two heuristics and conduct extensive simulations to study their performance when we aim to minimize the total assigned power of all nodes. The author is partially supported by NSF CCR-0311174.     

On optimal placement of relay nodes for reliable connectivity in wireless sensor networks

The paper addresses the relay node placement problem in two-tiered wireless sensor networks. Given a set of sensor nodes in Euclidean plane, our objective is to place minimum number of relay nodes to forward data packets from sensor nodes to the sink, such that: 1) the network is connected, 2) the network is 2-connected. For case one, we propose a (6+ε)-approximation algorithm for any ε > 0 with polynomial running time when ε is fixed. For case two, we propose two approximation algorithms with (24+ε) and (6/T+12+ε), respectively, where T is the ratio of the number of relay nodes placed in case one to the number of sensors. We further extend the results to the cases where communication radiuses of sensor nodes and relay nodes are different from each other.     

Establishing symmetric connectivity in directional wireless sensor networks equipped with $$2\pi /3$$ antennas

In this paper, we study the antenna orientation problem concerning symmetric connectivity in directional wireless sensor networks. We are given a set of nodes each of which is equipped with one directional antenna with beam-width \(\theta = 2\pi /3\) and is initially assigned a transmission range 1 that yields a connected unit disk graph spanning all nodes. The objective of the problem is to compute an orientation of the antennas and to find a minimum transmission power range \(r=O(1)\) such that the induced symmetric communication graph is connected. We propose two algorithms that orient the antennas to yield symmetric connected communication graphs where the transmission power ranges are bounded by 6 and 5, which are currently the best results for this problem. We also study the performance of our algorithms through simulations.     

A robust branch-and-cut approach for the minimum-energy symmetric network connectivity problem

This paper considers the minimum-energy symmetric network connectivity problem (MESNC) in wireless sensor networks. The aim of the MESNC is to assign transmission power to each sensor node such that the resulting network, using only bidirectional links, is connected and the total energy consumption is minimized. We first present two new models of this problem and then propose new branch-and-cut algorithms. Based on an existing formulation, we present the first model by introducing additional constraints. These additional constraints allow us to relax certain binary variables to continuous ones and thus to reduce significantly the number of binary variables. Our second model strengthens the first one by adding an exponential number of lifted directed-connectivity constraints. We present two branch-and-cut procedures based on these proposed improvements. The computational results are reported and show that our approaches, using the proposed formulations, can efficiently solve instances with up to 120 nodes, which significantly improve our ability to solve much larger instances in comparison with other exact algorithms in the literature.     

Relay node placement in two-tiered wireless sensor networks with base stations

This paper addresses the relay node placement problem in two-tiered wireless sensor networks with base stations, which aims to deploy a minimum number of relay nodes to achieve certain coverage and connectivity requirement. Under the assumption that the communication range of the sensor nodes is no more than that of the relay node, we present a polynomial time (5+?)-approximation algorithm for the 1-coverage 1-connected problem. Furthermore, we consider the fault tolerant problem in the network, we present a polynomial time (20+?)-approximation algorithm for the 2-coverage 2-connected problem, where ? is any given positive constant. For the k-coverage 2-connected situation, we present a polynomial time (15k?10+?)-approximation algorithm.     

Transport schemes for topology-transparent scheduling

Transport protocols provide reliable, end-to-end communication between a source and a destination in a network. The Transmission Control Protocol (TCP) uses backward error correction, where the destination explicitly returns feedback to the source. Forward error correction (FEC) can also be used for transport; here the source includes enough redundancy in the encoding symbols to allow the destination to decode the message. In this paper, we compare the performance of two transport schemes, TCP and LT, a scheme based on rateless FEC codes, in a wireless ad hoc network when topology-transparent scheduling is used for channel access. These schedules are derived from cover-free families, a type of combinatorial design. They provide a mechanism to guarantee collision-free communication between any two nodes provided that each of the N nodes of the network has at most a specified number D of active (transmitting) neighbours. We find that LT outperforms TCP in more strenuous network conditions. To Frank Hwang on the occasion of his sixty-fifth birthday.     

Domination in graphs with bounded propagation: algorithms,formulations and hardness results

We introduce a hierarchy of problems between the Dominating Set problem and the Power Dominating Set (PDS) problem called the ℓ-round power dominating set (ℓ-round PDS, for short) problem. For ℓ=1, this is the Dominating Set problem, and for ℓ≥n−1, this is the PDS problem; here n denotes the number of nodes in the input graph. In PDS the goal is to find a minimum size set of nodes S that power dominates all the nodes, where a node v is power dominated if (1) v is in S or it has a neighbor in S, or (2) v has a neighbor u such that u and all of its neighbors except v are power dominated. Note that rule (1) is the same as for the Dominating Set problem, and that rule (2) is a type of propagation rule that applies iteratively. The ℓ-round PDS problem has the same set of rules as PDS, except we apply rule (2) in “parallel” in at most ℓ−1 rounds. We prove that ℓ-round PDS cannot be approximated better than 2^log1-en2^{\log^{1-\epsilon}{n}} even for ℓ=4 in general graphs. We provide a dynamic programming algorithm to solve ℓ-round PDS optimally in polynomial time on graphs of bounded tree-width. We present a PTAS (polynomial time approximation scheme) for ℓ-round PDS on planar graphs for l = O(\fraclognloglogn)\ell=O(\frac{\log{n}}{\log{\log{n}}}) . Finally, we give integer programming formulations for ℓ-round PDS.     

On the Hardness of Approximating the Min-Hack Problem

We show several hardness results for the Minimum Hacking problem, which roughly can be described as the problem of finding the best way to compromise a target node given a few initial compromised nodes in a network. We give several reductions to show that Minimum Hacking is not approximable to within where δ = 1− ^c n, for any c < 1/2. We also analyze some heuristics on this problem.     

OMEGa: an optimistic most energy gain method for minimum energy multicasting in wireless ad hoc networks

In wireless ad hoc networks where every device runs on its own battery, the energy consumption is critical to lengthen the network lifetime. The communication among devices in the network can be categorized as unicasting and multicasting (including broadcasting). For the case of unicasting, computing the energy optimal path between the two communicating nodes is polynomially solvable by computing the shortest path. But for the case of multicasting, shortest path or minimum spanning tree does not guarantee an energy optimal communication. In this paper, we present our novel approach, Optimistic Most Energy Gain (OMEGa) method, for the minimum energy multicasting in wireless ad hoc networks. OMEGa aims at maximum utilization of Wireless Multicast Advantage (WMA), which essentially means covering more nodes by using larger energy. Both theoretical and experimental analysis shows OMEGa method performs very well. Research is partially supported by NSF and Air Force grants.     

Exact and heuristic algorithms for solving the generalized minimum filter placement problem

We consider a problem of placing route-based filters in a communication network to limit the number of forged address attacks to a prescribed level. Nodes in the network communicate by exchanging packets along arcs, and the originating node embeds the origin and destination addresses within each packet that it sends. In the absence of a validation mechanism, one node can send packets to another node using a forged origin address to launch an attack against that node. Route-based filters can be established at various nodes on the communication network to protect against these attacks. A route-based filter examines each packet arriving at a node, and determines whether or not the origin address could be legitimate, based on the arc on which the packet arrives, the routing information, and possibly the destination. The problem we consider seeks to find a minimum cardinality subset of nodes to filter so that the prescribed level of security is achieved. We formulate a mixed-integer programming model for the problem and derive valid inequalities for this model by identifying polynomially-solvable subgraphs of the communication network. We also present three heuristics for solving the filter placement problem and evaluate their performance against the optimal solution provided by the mixed-integer programming model. The authors gratefully acknowledge the comments of two anonymous referees, whose input led to an improved version of this paper. Dr. Smith gratefully acknowledges the support of the Office of Naval Research under Grant #N00014-03-1-0510 and the Defense Advanced Research Projects Agency under Grant #N66001-01-1-8925.     

An online distributed gossiping protocol for mobile networks

Gossiping in a communication network has long been studied as a combinatorial optimization problem in graphs under many different objective functions and communication models. In this paper, we propose a new online distributed gossiping protocol in the multicasting communication environment, where each node knows only its immediate neighbors. We show that the protocol can tolerate multiple node and link faults, mobility of nodes in the network (as long as the network remains connected) and it is more efficient than the a recently proposed protocol. The research reported in this paper is supported by NSF grant # ANI-0218495.     

Bounded information dissemination in multi-channel wireless networks

More and more wireless networks and devices now operate on multiple channels, which poses the question: How to use multiple channels to speed up communication? In this paper, we answer this question for the case of wireless ad-hoc networks where information dissemination is a primitive operation. Specifically, we propose a randomized distributed algorithm for information dissemination that is very near the optimal. The general information dissemination problem is to deliver \(k\) information packets, stored initially in \(k\) different nodes (the packet holders), to all the nodes in the network, and the objective is to minimize the time needed. With an eye toward the reality, we assume a model where the packet holders are determined by an adversary, and neither the number \(k\) nor the identities of packet holders are known to the nodes in advance. Not knowing the value of \(k\) sets this problem apart from broadcasting and all-to-all communication (gossiping). We study the information dissemination problem in single-hop networks with bounded-size messages. We present a randomized algorithm which can disseminate all packets in \(O(k(\frac{1}{\mathcal {F}}+\frac{1}{\mathcal {P}})+\log ^2n)\) rounds with high probability, where \(\mathcal {F}\) is the number of available channels and \(\mathcal {P}\) is the bound on the number of packets a message can carry. Compared with the lower bound \(\varOmega (k(\frac{1}{\mathcal {F}}+\frac{1}{\mathcal {P}}))\), the given algorithm is very close to the asymptotical optimal except for an additive factor. Our result provides the first solid evidence that multiple channels can indeed substantially speed up information dissemination, which also breaks the \(\varOmega (k)\) lower bound that holds for single-channel networks (even if \(\mathcal {P}\) is infinity).     

Minimizing the maximum travel time in a combined model of facility location and network design

This paper presents a combined Facility Location/Network Design Problem which simultaneously considers the location of facilities and the design of its underlying network so as to minimize the maximum customer-facility travel time. The model generalizes the classical p-center problem and has various applications in regional planning, distribution, telecommunications, emergency systems, and other areas. Two mixed integer programming formulations are presented and compared. Several valid inequalities are derived for the most promising of these formulations to strengthen its LP relaxation bound and to reduce the enumeration tree. Numerical results of a series of computational experiments for instances with up to 100 nodes and 500 candidate links are reported.     

Dispatching design for storage-centric wireless sensor networks

In a large-scale storage-centric wireless sensor network (SWSN) where data from different clusters are archived at distributed storage nodes, the dispatching design problem is to determine one or multiple storage nodes for each cluster. To achieve high data fidelity in SWSNs, the dispatching design should aim to reduce the data loss due to the network congestion and, at the same time, to prolong the network lifetime by avoiding sending excessive traffic to some particular storage nodes in order to achieve energy consumption balance among the relaying sensors around the storage node. In this paper, we propose an h-peak dispatching design for SWSN. Under such a design, regular traffic volume from each cluster will receive guaranteed data fidelity, and over-expectation traffic will receive best-effort data fidelity. We use an h-peak model to characterize the traffic deviation which assumes that at most h clusters may have over-expectation traffic simultaneously at a storage node. By incorporating h into the dispatching decision rather than assuming that all clusters may reach their traffic spikes simultaneously, the proposed h-peak dispatching design can achieve high data fidelity in SWSNs.     

Exact approaches for the directed network design problem with relays

We study the directed network design problem with relays (DNDPR) whose aim is to construct a minimum cost network that enables the communication of a given set of origin-destination pairs. Thereby, expensive signal regeneration devices need to be placed to cover communication distances exceeding a predefined threshold. Applications of the DNDPR arise in telecommunications and transportation. We propose two new integer programming formulations for the DNDPR. The first one is a flow-based formulation with a pseudo-polynomial number of variables and constraints and the second is a cut-based formulation with an exponential number of constraints. Fractional distance values are handled efficiently by augmenting both models with an exponentially-sized set of infeasible path constraints. We develop branch-and-cut algorithms and also consider valid inequalities to strengthen the obtained dual bounds and to speed up convergence. The results of our extensive computational study on diverse sets of benchmark instances show that our algorithms outperform the previous state-of-the-art method based on column generation.     

Using branch-and-price approach to solve the directed network design problem with relays

We present node-arc and arc-path formulations, and develop a branch-and-price approach for the directed network design problem with relays (DNDR). The DNDR problem can be used to model many network design problems in transportation, service, and telecommunication system, where relay points are necessary. The DNDR problem consists of introducing a subset of arcs and locating relays on a subset of nodes such that in the resulting network, the total cost (arc cost plus relay cost) is minimized, and there exists a directed path linking the origin and destination of each commodity, in which the distances between the origin and the first relay, any two consecutive relays, and the last relay and the destination do not exceed a predefined distance limit. With the node-arc formulation, we can directly solve small DNDR instances using mixed integer programming solver. With the arc-path formulation, we design a branch-and-price approach, which is a variant of branch-and-bound with bounds provided by solving linear programs using column generation at each node of the branch-and-bound tree. We design two methods to efficiently price out columns and present computational results on a set of 290 generated instances. Results demonstrate that our proposed branch-and-price approach is a computationally efficient procedure for solving the DNDR problem.     

On dual power assignment optimization for biconnectivity

Topology control is an important technology of wireless ad hoc networks to achieve energy efficiency and fault tolerance. In this paper, we study the dual power assignment problem for 2-edge connectivity and 2-vertex connectivity in the symmetric graphical model which is a combinatorial optimization problem from topology control technology.The problem is arisen from the following origin. In a wireless ad hoc network where each node can switch its transmission power between high-level and low-level, how can we establish a fault-tolerantly connected network topology in the most energy-efficient way? Specifically, the objective is to minimize the number of nodes assigned with high power and yet achieve 2-edge connectivity or 2-vertex connectivity.We addressed these optimization problems (2-edge connectivity and 2-vertex connectivity version) under the general graph model in (Wang et al. in Theor. Comput. Sci., 2008). In this paper, we propose a novel approximation algorithm, called Candidate Set Filtering algorithm, to compute nearly-optimal solutions. Specifically, our algorithm can achieve 3.67-approximation ratio for both 2-edge connectivity and 2-vertex connectivity, which improves the existing 4-approximation algorithms for these two cases.     

节点集重要性测度——综合法及其在知识共享网络中的应用

在具有社会关系结构的经济系统及通讯网络系统等许多现实的系统中,人们经常关注节点集在系统中的重要性问题.在分析如何有效反映网络中节点集重要性的基础上,针对节点赋权网络,利用节点集删除的研究方法,建立节点集重要性的综合测度数学模型;然后,借助于图的距离矩阵的计算方法设计该模型的算法;最后,给出该方法在知识共享网中的应用.     

Reliable Supply Chain Network Design

Risk management in supply chains has been receiving increased attention in the past few years. In this article, we present formulations for the strategic supply chain network design problem with dual objectives, which usually conflict with each other: minimizing cost and maximizing reliability. Quantifying the total reliability of a network design is not as straightforward as total cost calculation. We use reliability indices and develop analytical formulations that model the impact of upstream supply chain on individual entities’ reliability to quantify the total reliability of a network. The resulting multiobjective nonlinear model is solved using a novel hybrid algorithm that utilizes a genetic algorithm for network design and linear programming for network flow optimization. We demonstrate the application of our approach through illustrative examples in establishing tradeoffs between cost and reliability in network design and present managerial implications.