Minimum-Energy Broadcasting in Static Ad Hoc Wireless Networks

We present a new approximation algorithm for the Minimum Energy Broadcast Routing (MEBR) problem in ad hoc wireless networks that achieves an exponentially better approximation factor compared to the well-known Minimum Spanning Tree (MST) heuristic. Namely, for any instance where a minimum spanning tree of the set of stations is guaranteed to cost at most ρ ≥ 2 times the cost of an optimal solution for MEBR, we prove that our algorithm achieves an approximation ratio bounded by 2lnρ-2 ln 2 + 2. This result is particularly relevant for its consequences on Euclidean instances where we significantly improve previous results. In this respect, our experimental analysis confirms the better performance of the algorithm also in practice.

In this paper, we propose to address the energy efficient routing problem in multi-hop wireless networks with accumulative relay. In the accumulative relay model, partially overheard signals of previous transmissions for the same packet are used to decode it using a maximal ratio combiner technique [J.G. Proakis, 2001]. Therefore, additional energy saving can be achieved over traditional energy efficient routing. The idea of accumulative relay originates from the study of relay channel in information theory with a main focus on network capacity. It has been independently applied to minimum-energy broadcasting in L.G. Manish Agrawal et al. (2004), I. Maric and R. Yates (2002). We formulate the minimum energy accumulative routing problem (MEAR) and study it. We obtain hardness of approximation results counterbalanced with good heuristic solutions which we validate using simulations. Without energy accumulation, the classic shortest path (SP) algorithm finds the minimum energy path for a source-destination pair. However, we show that with energy accumulation, the SP can be arbitrarily bad. We turn our attention to heuristics and show that any optimal solution of MEAR can be converted to a canonical form - wave path. Armed with this insight, we develop a polynomial time heuristic to efficiently search over the space of all wavepaths. Simulation results show that our heuristic can provide more than 30% energy saving over minimum energy routing without accumulative relay. We also discuss the implementation issues of such a scheme.

We consider a setting where we are given a graph \(\mathcal {G}=(\mathcal {R},E)\), where \(\mathcal {R}=\{R_1,\ldots ,R_n\}\) is a set of polygonal regions in the plane. Placing a point \(p_i\) inside each region \(R_i\) turns \(G\) into an edge-weighted graph \(G_{\varvec{p}}\), \({\varvec{p}}=\{p_1,\ldots ,p_n\}\), where the cost of \((R_i,R_j)\in E\) is the distance between \(p_i\) and \(p_j\). The Shortest Path Problem with Neighborhoods asks, for given \(R_s\) and \(R_t\), to find a placement \(\varvec{p}\) such that the cost of a resulting shortest \(st\)-path in \(\mathcal {G}_{\varvec{p}}\) is minimum among all graphs \(\mathcal {G}_{\varvec{p}}\). The Minimum Spanning Tree Problem with Neighborhoods asks to find a placement \(\varvec{p}\) such that the cost of a resulting minimum spanning tree is minimum among all graphs \(\mathcal {G}_{\varvec{p}}\). We study these problems in the \(L_1\) metric, and show that the shortest path problem with neighborhoods is solvable in polynomial time, whereas the minimum spanning tree problem with neighborhoods is \(\mathsf {APX}\)-hard, even if the neighborhood regions are segments.

We consider a setting where we are given a graph $$\mathcal {G}=(\mathcal {R},E)$$ , where $$\mathcal {R}=\{R_1,\ldots ,R_n\}$$ is a set of polygonal regions in the plane. Placing a point $$p_i$$ inside each region $$R_i$$ turns $$G$$ into an edge-weighted graph $$G_{\varvec{p}}$$ , $${\varvec{p}}=\{p_1,\ldots ,p_n\}$$ , where the cost of $$(R_i,R_j)\in E$$ is the distance between $$p_i$$ and $$p_j$$ . The Shortest Path Problem with Neighborhoods asks, for given $$R_s$$ and $$R_t$$ , to find a placement $$\varvec{p}$$ such that the cost of a resulting shortest $$st$$ -path in $$\mathcal {G}_{\varvec{p}}$$ is minimum among all graphs $$\mathcal {G}_{\varvec{p}}$$ . The Minimum Spanning Tree Problem with Neighborhoods asks to find a placement $$\varvec{p}$$ such that the cost of a resulting minimum spanning tree is minimum among all graphs $$\mathcal {G}_{\varvec{p}}$$ . We study these problems in the $$L_1$$ metric, and show that the shortest path problem with neighborhoods is solvable in polynomial time, whereas the minimum spanning tree problem with neighborhoods is $$\mathsf {APX}$$ -hard, even if the neighborhood regions are segments.

—Wireless ad hoc networks are usually composed of autonomous nodes, which are powered by batteries only. The energy-efficiency is perhaps one of the most important factors for each operation in terms of networks. Broadcast, for example, is one of the fundamental operations in modern telecom networks. In this paper a broadcast tree, which is rooted at a source and spans all the destination nodes, has been constructed in a way that the total transmission energy consumption is minimized. This paper describes two polynomial-time heuristics for the energy-efficient broadcasting in static ad hoc wireless networks. Both of the developed approaches are on the basis of a fuzzy greedy evaluation function, which prioritize the network nodes. According to the prioritized order of the nodes, each new node is selected for incorporation in the construction of a solution. Computational experiments indicate that our algorithms improve the well-known Broadcast Link-based Minimum Spanning Tree (BLiMST) and Broadcast Least-Unicast-cost (BLU) heuristics. It will be seen that the BLiMST and the BLU methods are a special case of our more general heuristics.

In this paper, we address the problem of multicast routing in mobile ad-hoc networks from the viewpoint of energy efficiency. In an ad-hoc wireless network, each node runs on a local energy source which has a limited energy life span. Thus, energy conservation is a critical issue in mobile ad-hoc networks. One approach for energy conservation is to establish routes that require lowest total energy consumption. This optimization problem is referred as the minimum-energy multicast routing problem (MEMRP). In this paper, propose new efficient heuristic algorithms for the construction of energy-efficient multicast routes in mobile ad-hoc networks. These algorithms exploit the broadcast nature of the wireless channel, and address the need for energy-efficient operations. Empirical studies show that our algorithms are able to achieve better performance than algorithms that have been developed for MEMRP.

This study’s objective is to assess the performance of routing processing between Shortest Paths Tree (SPT) and Minimum Spanning Tree (MST). In this paper we propose and create software to calculate the efficiency path of routing processing in the network. Extensive simulations are being carried out with two different algorithms specific for Dijkistra’s algorithm and Kruskal’s algorithm. The network loads in the performance plots are characterized by two important parameters (a number of vertices) - 7 nodes and 10 nodes, more vertices could show good performance in the simulation results and showed that the performance of Kruskal’s algorithm is better than Dijkistra’s algorithm when the network loads are increased from 7 nodes to 10 nodes. In this simulation, Because of the total cost of distance matrix for Kruskal is less than Dijkistra when the number of routers or nodes is increased from 7 nodes to 10 nodes. This software namely Network Aids Design (NAD), is useful for calculation about the performance of routing processing in the network.

2008 14th IEEE International Conference on Parallel and Distributed Systems, ICPADS'08, Melbourne, VIC, 8-10 December 2008

Distributed ant colony optimization for minimum energy broadcasting in sensor networks with realistic antennas

Motivated by the increasing need for fast distributed processing of large-scale graphs such as the Web graph and various social networks, we study a number of fundamental graph problems in the message-passing model, where we have k machines that jointly perform computation on an arbitrary n-node (typically, n > k) input graph. The graph is assumed to be randomly partitioned among the k ≥ 2 machines (a common implementation in many real world systems). The communication is point-to-point, and the goal is to minimize the time complexity i.e., the number of communication rounds, of solving various fundamental graph problems.We present lower bounds that quantify the fundamental time limitations of distributively solving graph problems. We first show a lower bound of Ω(n/k) rounds for computing a spanning tree (ST) of the input graph. This result also implies the same bound for other fundamental problems such as computing a minimum spanning tree (MST), breadth-first tree (BFS), and shortest paths tree (SPT). We also show an Ω(n/k2) lower bound for connectivity ST verification and other related problems. Our lower bounds develop and use new bounds in random-partition communication complexity.To complement our lower bounds, we also give algorithms for various fundamental graph problems, e.g., PageRank, MST, connectivity, ST verification, shortest paths, cuts, spanners, covering problems, densest subgraph, subgraph isomorphism, finding triangles, etc. We show that problems such as PageRank, MST, connectivity, and graph covering can be solved in O(n/k) time (the notation O hides polylog(n) factors and an additive polylog(n) term); this shows that one can achieve almost linear (in k) speedup, whereas for shortest paths, we present algorithms that run in O(n/Ok) time (for (1 + e)-factor approximation) and in O(n/k) time (for O(log n)-factor approximation) respectively.Our results are a step towards understanding the complexity of distributively solving large-scale graph problems.

One of the key issues in providing end-to-end quality of service (QoS) guarantees in today's networks is how to determine a feasible route that satisfies a set of constraints. In general, finding a path subject to multiple constraints is an NP-complete problem that cannot be exactly solved in polynomial time. Accordingly, several heuristics and approximation algorithms have been proposed for this problem. Many of these algorithms suffer from either excessive computational cost or low performance. In this paper, we propose a fuzzy-logic based algorithm for finding a bandwidth-delay-constrained path by Dijkstra's shortest path algorithm. The main objective of Fuzzy QOS Routing Algorithm (FQRA) is to reduce packet loss and increase overall network utilization. To achieve this objective, the algorithm at First, eliminates all links with a bandwidth less than the requirement so that any paths in the resulting graph will satisfy the bandwidth constraint. Then, a new single parameter with the aid of Fuzzy Logic is generated from inputs bandwidth and delay. The Shortest path calculated by Dijkstra's algorithm based on new metric. Simulation results show that FQRA outperforms several earlier algorithms in terms of overall network utilization and packet loss. The worst-case computational complexity of this algorithm is within a logarithmic number of calls to Dijkstra's shortest path algorithm, equal with O(n2) for a network graph with n nodes.

Various network monitoring and performance evaluation schemes generate considerable amount of traf- fic, which affects network performance. In this paper we describe a method for minimizing network monitoring overhead based on Shortest Path Tree (SPT) protocol. We describe two different variations of the problem: the A Problem and the E -Problem and prove that finding optimal solutions for both A - and E -problems is NP -hard. We also show that in general, an A -problem solution requires a significantly higher network overhead than an E -problem solution. We propose optimal approximation algorithms for the A - and E -problems and few different heuristics for the E -problem. Namely, we show that one can compute in polynomial time an O(ln|V |) -approximate solution for each of these problems. We analyze the performance of our approximation algorithms and heuristics on large graphs generated using Power-Law model. Performance results show that our heuristic algorithms for both problems achieve from 50% to 90% improvement in the network overhead comparatively with earlier algorithms that appeared in literature.

Compressive sensing (CS) can reduce the number of data transmissions and balance the traffic load throughout networks. However, the total number of data transmissions required in CS method is still large. It is observed that there are many zero elements in the measurement matrix. In each round of data transmission in CS method, the sensor nodes corresponding to the zero elements in the measurement matrix do not have their own data to transmit. To further reduce the number of data transmissions in the network, we aim to compute a data gathering tree by taking advantages of these zero elements in the measurement matrix, such that the total number of data transmissions is minimized. We formulate the problem as linear programming with boolean variables. The problem is NP-hard. We propose heuristic algorithm to compute the Minimum Transmission Tree (MTT) for data gathering in CS methods. The MTT algorithm constructs a spanning tree by iteratively including the edge whose average incremental transmission cost is minimum. The simulation results demonstrate that our algorithm can reduce the number of transmissions significantly, compared with the methods using minimum spanning tree (MST), shortest path tree and the CS method with nonzero measurement coefficient using MST.

In this paper we study the minimum total energy and maximum network lifetime routing problem in wireless ad hoc networks. We develop competitive online schemes for an infinite sequence of random routing requests with provable approximation factors in both measures. In addition, we produce fundamental bounds on the expected total energy consumption and network lifetime in the optimal offline solution. Our results are verified through simulations. In the course of our analysis we derive an interesting property of shortest path trees (SPT) for a random point process. We show that the maximum edge length of any SPT is asymptotically equal to the maximum edge length of a minimum spanning tree. This result is of self interest for the study of energy efficient routing as many heuristics rely on SPTs.

When transport in networks follows the shortest paths, the union of all shortest path trees G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋃spt</sub> can be regarded as the "transport overlay network". Overlay networks such as peer-to-peer networks or virtual private networks can be considered as a subgraph of G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋃spt</sub> . We construct two types of G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋃spt</sub> : (a) G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋃spt(α)</sub> where α is the extreme value index of polynomial link weights and (b) G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋃spt(ρ)</sub> where ρ is the correlation coefficient of the 2-dimensional correlated uniformly distributed link weights in QoS routing. By tuning the extreme value index α of polynomial link weights, a phase transition occurs around a critical extreme value index α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> of the link weight distribution. If α > α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , transport in the network traverses many links whereas for α < α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , all transport flows over a critical backbone: the minimum spanning tree (MST). In QoS routing with 2-dimensional link weights, as we decrease the correlation coefficient ρ from 1 to -1, the overlay G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋃spt</sub> becomes denser, and is equal to the substrate when ρ = -1. With the Erdos-Renyi random graph as the underlying topology, we show that the overlay G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⋃spt(ρ)</sub> is also close to an Erdos-Renyi random graph G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> (N), an observation with potential for mobile and wireless ad-hoc networks. The existence of such a controllable transition in the overlay structure may allow network operators to steer and balance flows in their network.