Gruia Calinescu

Minimum-energy broadcast routing in static ad hoc wireless networks

Energy conservation is a critical issue in ad hoc wireless networks for node and network life, as the nodes are powered by batteries only. One major approach for energy conservation is to route a communication session along the routes which requires the lowest total energy consumption. This optimization problem is referred to as minimum-energy routing. While minimum-energy unicast routing can be solved in polynomial time by shortest-path algorithms, it remains open whether minimum-energy broadcast routing can be solved in polynomial time, despite the NP-hardness of its general graph version. Previously three greedy heuristics were proposed in Wieselthier et al. (2000): MST (minimum spanning tree), SPT (shortest-path tree), and BIP (broadcasting incremental power). They have been evaluated through simulations in Wieselthier et al.], but little is known about their analytical performance. The main contribution of this paper is the quantitative characterization of their performances in terms of approximation ratios. By exploring geometric structures of Euclidean MSTs, we have been able to prove that the approximation ratio of MST is between 6 and 12, and the approximation ratio of BIP is between /sup 13///sub 3/ and 12. On the other hand, the approximation ratio of SPT is shown to be at least /sup n///sub 2/, where n is the number of receiving nodes. To our best knowledge, these are the first analytical results for minimum-energy broadcasting.

Maximizing a Monotone Submodular Function Subject to a Matroid Constraint

An improved coating pan apparatus and spray arm assembly are disclosed for providing facilitated maintenance and cleaning of sensitive spray nozzles. The spray arm assembly includes means for varying the spray length and spray angle from a position external to the coating drum. Additionally, this invention provides adjustment means for removing the fixture containing the spray nozzles entirely from the coating drum and laterally from the coating apparatus housing for purging.

Distributed construction of a planar spanner and routing for ad hoc wireless networks

Several localized routing protocols (see Bose, P. and Morin, P., Proc. 10th Annual Int. Symp. on Algorithms and Computation ISAAC, 1999) guarantee the delivery of packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we more accurately model the network as a unit-disk graph, UDG, in which a link between two nodes exists only if the distance between them is at most the maximum transmission range. Given a graph H, a spanning subgraph G of H is a t-spanner if the length of the shortest path connecting any two points in G is no more than t times the length of the shortest path connecting the two points in H. We present a novel localized networking protocol that constructs a planar 2.5-spanner of UDG, called the localized Delaunay triangulation, as network topology. It contains all edges that are in both the UDG and the Delaunay triangulation of all wireless nodes. Our experiments show that the delivery rates of existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. The total communication cost of our networking protocol is O(n log n) bits. Moreover, the computation cost of each node u is O(d/sub u/ log d/sub u/), where d/sub u/ is the number of 1-hop neighbors of u in UDG.

Localized Delaunay triangulation with application in ad hoc wireless networks

Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RING) or Gabriel graph (GG) is used as such planar structure. However, it is well-known that the spanning ratios of these two graphs are not bounded by any constant (even for uniform randomly distributed points). Bose et al. (1999) recently developed a localized routing protocol that guarantees that the distance traveled by the packets is within a constant factor of the minimum if Delaunay triangulation of all wireless nodes is used, in addition, to guarantee the delivery of the packets. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we model the network as a unit-disk graph (UDG), in which a link uv exists only if the distance /spl par/uv/spl par/ is at most the maximum transmission range. In this paper, we present a novel localized networking protocol that constructs a planar 2 5-spanner of UDG, called the localized Delaunay triangulation (LDEL), as network topology. It contains all edges that are both in the unit-disk graph and the Delaunay triangulation of all nodes. The total communication cost of our networking protocol is O(n log n) bits, which is within a constant factor of the optimum to construct any structure in a distributed manner. Our experiments show that the delivery rates of some of the existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. Our simulations also show that the traveled distance of the packets is significantly less when the FACE routing algorithm is applied on LDEL, rather than applied on GG.

Power efficient monitoring management in sensor networks

Optimizing the energy consumption in wireless sensor networks has recently become the most important performance objective. We assume the sensor network model in which sensors can interchange idle and active modes. Given monitoring regions, battery life and energy consumption rate for each sensor, we formulate the problem of maximizing sensor network lifetime, i.e., time during which the monitored area is (partially or fully) covered. Our contributions include (1) an efficient data structure to represent the monitored area with at most n/sup 2/ points guaranteeing the full coverage which is superior to the previously used approach based on grid points, (2) efficient provably good centralized algorithms for sensor monitoring schedule maximizing the total lifetime including (1+ln(1-q)/sup -1/)-approximation algorithm for the case when a q-portion of the monitored area is required to cover, e.g., for the 90% area coverage our schedule guarantees to be at most 3.3 times shorter than the optimum, (4) a family of efficient distributed protocols with trade-off between communication and monitoring power consumption, (5) extensive experimental study of the proposed algorithms showing significant advantage in quality, scalability and flexibility.

Network Lifetime and Power Assignment in ad hoc wireless networks

Used for topology control in ad-hoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G=(V,c). The power of a vertex u in a directed spanning subgraph H is given by PH (u) = max uv ∈ E(H) c(uv). The power of H is given by \(p(H) = \sum_{u \in v}p{\sc H}(u)\), Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. We present asymptotically optimal O(log n)-approximation algorithms for three Power Assignment problems: Min-Power Strong Connectivity, Min-Power Symmetric Connectivity (the undirected graph having an edge uv iff H has both uv and vu must be connected) and Min-Power Broadcast (the input also has r ∈ V , and H must be a r-rooted outgoing spanning arborescence).

Grooming of arbitrary traffic in SONET/WDM BLSRs

SONET add-drop multiplexers (ADMs) are the dominant cost factor in the SONET/WDM rings. They can potentially be reduced by optical bypass via optical add-drop multiplexers (OADMs) and traffic grooming. In this paper we study the grooming of arbitrary traffic in WDM bidirectional line-switched rings (BLSRs) so as to minimize the ADM cost. Two versions of the minimum ADM cost problem are addressed. In the first version, each traffic stream has a predetermined routing. In the second version, the routing of each traffic stream is not given in advance; however, each traffic stream is fully duplex with symmetric demands, which must be routed along the same path but in opposite directions. In both versions, we further consider two variants depending on whether a traffic stream is allowed to be split at intermediate nodes. All the four combinations are NP-hard even for any fixed line-speed. General lower bounds on the minimum ADM cost are provided. Our traffic grooming follows a two-phased approach. The problem targeted at in each phase is NP-hard itself, except the second phase when the line speed is two. Various approximation algorithms are proposed in both phases, and their approximation ratios are analyzed.

Symmetric Connectivity with Minimum Power Consumption in Radio Networks

We study the problem of assigning transmission ranges to the nodes of a multi-hop packet radio network (also known as static ad hoc wireless network) so as to minimize the total power consumed under the constraint that enough power is provided to the nodes to ensure that the network is connected. Precisely, we require that the bidirectional links established by the transmission range of every node form a connected graph. We call this problem Min-Power Symmetric Connectivity.

Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)

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Approximation Algorithms for the 0-Extension Problem

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