Results 1  10
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34
AdHoc Networks Beyond Unit Disk Graphs
, 2003
"... In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer ..."
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Cited by 105 (10 self)
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In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that  in comparison to the cost known on Unit Disk Graphs  the complexity results in this model contain the additional factor 1/d&sup2;. We prove that in Quasi Unit Disk Graphs flooding is an asymptotically messageoptimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.
Topology Control meets SINR: The Scheduling Complexity of Arbitrary Topologies
 In Proc. of the 7 th ACM Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC
, 2006
"... To date, topology control in wireless ad hoc and sensor networks—the study of how to compute from the given communication network a subgraph with certain beneficial properties—has been considered as a static problem only; the time required to actually schedule the links of a computed topology withou ..."
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Cited by 75 (9 self)
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To date, topology control in wireless ad hoc and sensor networks—the study of how to compute from the given communication network a subgraph with certain beneficial properties—has been considered as a static problem only; the time required to actually schedule the links of a computed topology without message collision was generally ignored. In this paper we analyze topology control in the context of the physical SignaltoInterferenceplusNoiseRatio (SINR) model, focusing on the question of how and how fast the links of a resulting topology can actually be realized over time. For this purpose, we define and study a generalized version of the SINR model and obtain theoretical upper bounds on the scheduling complexity of arbitrary topologies in wireless networks. Specifically, we prove that even in worstcase networks, if the signals are transmitted with correctly assigned transmission power levels, the number of time slots required to successfully schedule all links of an arbitrary topology is proportional to the squared logarithm of the number of network nodes times a previously defined static interference measure. Interestingly, although originally considered without explicit accounting for signal collision in the SINR model, this static interference measure plays an important role in the analysis of link scheduling with physical link interference. Our result thus bridges the gap between static graphbased interference models and the physical SINR model. Based on these results, we also show that when it comes to scheduling, requiring the communication links to be symmetric may imply significantly higher costs as opposed to topologies allowing unidirectional links.
R.: The Complexity of Connectivity in Wireless Networks
 In: Proc. of the 25 th Annual Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM
, 2006
"... Abstract — We define and study the scheduling complexity in wireless networks, which expresses the theoretically achievable efficiency of MAC layer protocols. Given a set of communication requests in arbitrary networks, the scheduling complexity describes the amount of time required to successfully ..."
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Cited by 70 (13 self)
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Abstract — We define and study the scheduling complexity in wireless networks, which expresses the theoretically achievable efficiency of MAC layer protocols. Given a set of communication requests in arbitrary networks, the scheduling complexity describes the amount of time required to successfully schedule all requests. The most basic and important network structure in wireless networks being connectivity, we study the scheduling complexity of connectivity, i.e., the minimal amount of time required until a connected structure can be scheduled. In this paper, we prove that the scheduling complexity of connectivity grows only polylogarithmically in the number of nodes. Specifically, we present a novel scheduling algorithm that successfully schedules a strongly connected set of links in time O(log 4 n) even in arbitrary worstcase networks. On the other hand, we prove that standard MAC layer or scheduling protocols can perform much worse. Particularly, any protocol that either employs uniform or linear (a node’s transmit power is proportional to the minimum power required to reach its intended receiver) power assignment has a Ω(n) scheduling complexity in the worst case, even for simple communication requests. In contrast, our polylogarithmic scheduling algorithm allows many concurrent transmission by using an explicitly formulated nonlinear power assignment scheme. Our results show that even in largescale worstcase networks, there is no theoretical scalability problem when it comes to scheduling transmission requests, thus giving an interesting complement to the more pessimistic bounds for the capacity in wireless networks. All results are based on the physical model of communication, which takes into account that the signaltonoise plus interference ratio (SINR) at a receiver must be above a certain threshold if the transmission is to be received correctly. I.
DRAND: Distributed randomized TDMA scheduling for wireless ad hoc networks
 in MobiHoc
, 2006
"... This paper presents a distributed implementation of RAND, a randomized time slot scheduling algorithm, called DRAND. DRAND runs in O(δ) time and message complexity where δ is the maximum size of a twohop neighborhood in a wireless network while message complexity remains O(δ), assuming that message ..."
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Cited by 51 (1 self)
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This paper presents a distributed implementation of RAND, a randomized time slot scheduling algorithm, called DRAND. DRAND runs in O(δ) time and message complexity where δ is the maximum size of a twohop neighborhood in a wireless network while message complexity remains O(δ), assuming that message delays can be bounded by an unknown constant. DRAND is the first fully distributed version of RAND. The algorithm is suitable for a wireless network where most nodes do not move, such as wireless mesh networks and wireless sensor networks. We implement the algorithm in TinyOS and demonstrate its performance in a real testbed of Mica2 nodes. The algorithm does not require any time synchronization and is shown to be effective in adapting to local topology changes without incurring global overhead in the scheduling. Because of these features, it can also be used even for other scheduling problems such as frequency or code scheduling (for FDMA or CDMA) or local identifier assignment for wireless networks where time synchronization is not enforced.
Efficient InterferenceAware TDMA Link Scheduling for Static Wireless Networks
 In ACM MobiCom
, 2006
"... We study efficient link scheduling for a multihop wireless network to maximize its throughput. Efficient link scheduling can greatly reduce the interference effect of closeby transmissions. Unlike the previous studies that often assume a unit disk graph model, we assume that different terminals cou ..."
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Cited by 47 (7 self)
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We study efficient link scheduling for a multihop wireless network to maximize its throughput. Efficient link scheduling can greatly reduce the interference effect of closeby transmissions. Unlike the previous studies that often assume a unit disk graph model, we assume that different terminals could have different transmission ranges and different interference ranges. In our model, it is also possible that a communication link may not exist due to barriers or is not used by a predetermined routing protocol, while the transmission of a node always result interference to all nonintended receivers within its interference range. Using a mathematical formulation, we develop synchronized TDMA link schedulings that optimize the networking throughput. Specifically, by assuming known link capacities and link traffic loads, we study link scheduling under the RTS/CTS interference model and the protocol interference model with fixed transmission power. For both models, we present both efficient centralized and distributed algorithms that use time slots within a constant factor of the optimum. We also present efficient distributed algorithms whose performances are still comparable with optimum, but with much less communications. Our theoretical results are corroborated by extensive simulation studies.
Complexity in geometric sinr
 In MobiHoc
, 2007
"... In this paper we study the problem of scheduling wireless links in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NPcompleteness proofs in such a model. In particular, we prove two problems to be NPcomplete: Scheduli ..."
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Cited by 47 (1 self)
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In this paper we study the problem of scheduling wireless links in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NPcompleteness proofs in such a model. In particular, we prove two problems to be NPcomplete: Scheduling and OneShot Scheduling. The first problem consists in finding a minimumlength schedule for a given set of links. The second problem receives a weighted set of links as input and consists in finding a maximumweight subset of links to be scheduled simultaneously in one shot. In addition to the complexity proofs, we devise an approximation algorithm for each problem.
Selfstabilizing population protocols
 In Ninth International Conference on Principles of Distributed Systems
"... This paper studies selfstabilization in networks of anonymous, asynchronously interacting nodes where the size of the network is unknown. Constantspace protocols are given for Dijkstrastyle roundrobin token circulation, leader election in rings, 2hop coloring in degreebounded graphs, and estab ..."
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Cited by 35 (9 self)
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This paper studies selfstabilization in networks of anonymous, asynchronously interacting nodes where the size of the network is unknown. Constantspace protocols are given for Dijkstrastyle roundrobin token circulation, leader election in rings, 2hop coloring in degreebounded graphs, and establishing consistent global orientation in an undirected ring. A protocol to construct a spanning tree in regular graphs using O(log D) memory is also given, where D is the diameter of the graph. A general method for eliminating nondeterministic transitions from the selfstabilizing implementation of a large family of behaviors is used to simplify the constructions, and general conditions under which protocol composition preserves behavior are used in proving their correctness.
Maximal Independent Sets in Radio Networks
"... We study the distributed complexity of computing a maximal independent set (MIS) in radio networks with completely unknown topology, asynchronous wakeup, and no collision detection mechanism available. Specifically, we propose a novel randomized algorithm that computes a MIS in time O(log 2 n) with ..."
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Cited by 33 (7 self)
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We study the distributed complexity of computing a maximal independent set (MIS) in radio networks with completely unknown topology, asynchronous wakeup, and no collision detection mechanism available. Specifically, we propose a novel randomized algorithm that computes a MIS in time O(log 2 n) with high probability, where n is the number of nodes in the network. This significantly improving on the best previously known solutions. A lower bound of Ω(log 2 n / log log n) given in [11] implies that our algorithm’s running time is close to optimal. Our result shows that the harsh radio network model imposes merely an additional O(log n) factor compared to Luby’s MIS algorithm in the message passing model. This has important implications in the context of ad hoc and sensor networks whose characteristics are closely captured by the radio network model.
Modeling sensor networks
, 2008
"... In order to develop algorithms for sensor networks and in order to give mathematical correctness and performance proofs, models for various aspects of sensor networks are needed. This chapter presents and discusses currently used models for sensor networks. Generally, finding good models is a challe ..."
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Cited by 28 (5 self)
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In order to develop algorithms for sensor networks and in order to give mathematical correctness and performance proofs, models for various aspects of sensor networks are needed. This chapter presents and discusses currently used models for sensor networks. Generally, finding good models is a challenging task. On the one hand, a
Wireless scheduling with power control
 In Proc. 17th European Symposium on Algorithms (ESA
, 2009
"... We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that e ..."
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Cited by 23 (3 self)
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We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signaltointerferenceplusnoise (SINR) constraints. We give an algorithm that attains an approximation ratio of O(log n · log log Λ), where Λ is the ratio between the longest and the shortest linklength. Under the natural assumption that lengths are represented in binary, this gives the first polylog(n)approximation. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We show this dependence on Λ to be unavoidable, giving a construction for which any oblivious power assignment results in a Ω(log log Λ)approximation. We also give a simple online algorithm that yields a O(log Λ)approximation, by a reduction to the coloring of unitdisc graphs. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2dimensional Euclidean plane to doubling metrics. 1