Fig 2 - uploaded by Christian Scheideler
Content may be subject to copyright.
Source publication
Radio networks are widely used today. People access voice and data services via mobile phones, Bluetooth technology replaces
unhandy cables by wireless links, and wireless networking is possible via IEEE 802.11 compatible network equipment. Nodes
in such networks exchange their data packets usually with fixed base stations that connect them with a...
Similar publications
In this paper we present and analyze HSkip+, a self-stabilizing overlay
network for nodes with arbitrary heterogeneous bandwidths. HSkip+ has the same
topology as the Skip+ graph proposed by Jacob et al. [PODC 2009] but its
self-stabilization mechanism significantly outperforms the self-stabilization
mechanism proposed for Skip+. Also, the nodes ar...
Advantages of bringing small-world properties in mobile ad hoc networks (MANETs) in terms of quality of service has been studied and outlined in the past years. In this work, we focus on the specific class of vehicular ad hoc networks (VANETs) and propose to un-partition such networks and improve their small-world properties. To this end, a subset...
or via WWW at URL http://www.cs.unibo.it/. Plain-text abstracts organized by year are available in the directory ABSTRACTS. All local authors can be reached via e-mail at the address last-name[at]cs.unibo.it. Recent Titles from the UBLCS Technical Report Series 2003-5 Synchronized Hypermedia Documents: a Model and its Applications (Ph.D. Thesis), G...
Self-stabilization is the property of a system to transfer itself regardless of the initial state into a legitimate state. Chord as a simple, decentralized and scalable distributed hash table is an ideal showcase to introduce self-stabilization for p2p overlays. In this paper, we present Re-Chord, a self-stabilizing version of Chord. We show, that...
Information flow applications like distributed continual queries, online scientific collaboration and visualization, and the operational information systems used by large corporations involve the acquisition, processing, and dissemination of events across distributed computing platforms. Multiple distinct middleware frameworks have been developed t...
Citations
... Althöfer et al. [11] firstly proved that YGs are the t-spanners for the corresponding complete graph. For the corresponding complete graph, YGs are 1/ð1 − 2 sin ðπ/kÞÞ -spanners with k > 6 [12]. Wireless Communications and Mobile Computing ...
Following the recent advances in the Internet of Things (IoT), it is drawing lots of attention to design distributed algorithms for various network optimization problems under the SINR (Signal-to-Interference-and-Noise-Ratio) interference model, such as spanner construction. Since a spanner can maintain a linear number of links while still preserving efficient routes for any pair of nodes in wireless networks, it is important to design distributed algorithms for spanners. Given a constant t>1 as the required stretch factor, the problem of our concern is to design an efficient distributed algorithm to construct a t-spanner of the communication graph under SINR such that the delay for the task completion is minimized, where the delay is the time interval between the time slot that the first node commences its operation to the time slot that all the nodes finish their task of constructing the t-spanner. Our main contributions include four aspects. First, we propose a proximity range and proximity independent set (PISet) to increase the number of nodes transmitting successfully at the same time in order to reduce the delay. Second, we develop a distributed randomized algorithm SINR-Spanner to construct a required t-spanner with high probability. Third, the approximation ratio of SINR-Spanner is proven to be a constant. Finally, extensive simulations are carried out to verify the effectiveness and efficiency of our proposed algorithm.
... 4k + 3, 4k + 5 1 1−2 sin(3θ/8) [2] cos(θ/4) cos(θ/2)−sin(3θ/4 ) Interest in Yao and Theta graphs has increased with the advancement of wireless ad hoc networks and the need for efficient communication (see [26,28,21,15] and the references therein). Designing routing algorithms for wireless ad hoc networks is an extremely difficult task and research in this area is still in progress. ...
We study the spanning properties of Theta-Theta graphs. Similar in spirit
with the Yao-Yao graphs, Theta-Theta graphs partition the space around each
vertex into a set of k cones, for some fixed integer k > 1, and select at most
one edge per cone. The difference is in the way edges are selected. Yao-Yao
graphs select an edge of minimum length, whereas Theta-Theta graphs select an
edge of minimum orthogonal projection onto the cone bisector. It has been
established that the Yao-Yao graphs with parameter k = 6k' have spanning ratio
11.67, for k' >= 6. In this paper we establish a first spanning ratio of 5.51
for Theta-Theta graphs, for the same values of k. We also extend the class of
Theta-Theta spanners with parameter 6k', and establish a spanning ratio of 34.2
for any k' >= 4. We surmise that these stronger results are mainly due to a
tighter analysis in this paper, rather than Theta-Theta being superior to
Yao-Yao as a spanner. We also show that the spanning ratio of Theta-Theta
graphs decreases to 3.86 as k' increases to 8. These are the first results on
the spanning properties of Theta-Theta graphs.
... The specific abstract graph structures which allow us to mathematize and model these lines of new technologies are the families of graphs known as Yao graphs and Theta graphs and they are variants. In a detailed survey [34], Prof. Christian Scheideler has already discussed the power spanner and other type of spanning properties as applicable to the domain of wireless networks of various graphs. However, we did feel that given the volume of new emerging works and the use of directional antennas and adaptive beam forming, the Yao graph like structures and its variants got to be revisited in a fresh survey with a lot more detailed focus while contemplating adaptation of the same in conceptualization of new network optimization problems which in corporates the effect of these new technologies. ...
The advent of wireless communication and networking in the last two decades has led to the need of modification in the regular graphs used as spanners. The spanner is a sub graph of the original graph which connects the essential nodes for transmission of the message. For this purpose the Omni directional antennas are usually used and the "spanner-graph" performance metric is a constant multiplied by the same of the original graph. This constant is known as the "stretch factor". One of the most common attribute for wireless communication is the energy required for faithful transmission of a message between two nodes. But the Omni directional antennas lead to interference and wastage of bandwidth and energy. The nodes of wireless communication are however neither always static nor equipped with any infrastructure. Rather the same might as well be ad-hoc and mobile. Another well used notion is that of the unit disk graph (UDG), where a node can communicate INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL. 7, NO. 2, June 2014 only if the other nodes are within the disk of unit radius. However the graph being dynamic in nature, the nodes do not have fixed transmission radii and the same changes according to the power requirement of transmission. This work of ours mainly deals with the different graphs being used as spanners. It explains a few algorithms described in other papers which it reviewed. The associated algorithms are related to Yao graph. This graph and its modifications are discussed and it is explained how they could be used energy efficiently. The Yao-Yao graph for example can be used as a spanner for certain specific values of stretch factors.
... Topology control of wireless ad-hoc networks deployed in the plane is a fundamental problem in the area of wireless computing [23], [25], [26]. Topology control is used, for example, to construct a topology of the original network that is amenable to routing or other networking applications. ...
... Some desirable properties of the resulting topology include (1) planarity: the underlying graph should be planar to allow, for example, guaranteed and efficient routing such as geometric routing ( [5], [16]); (2) bounded stretch factor: for any two devices in the network there should be a path connecting them in the topology whose length is close to the length of the shortest path connecting the pair in the original network; (3) bounded degree: each device maintains links to only a constant number of devices in its communication range, thus minimizing interference and saving energy; and (4) constructible locally: the construction of the network topology should be distributed, simple, and strictly-localized in the sense that each point constructs and maintains its links in the topology based only on the information from neighboring devices without exchanging or propagating global information (see [7] for a formal definition). The problem of computing efficient topologies for ad-hoc wireless networks has been extensively considered in the literature [14], [18], [21], [23], [24], [25], [26], [28], [29], [32], [33], [34]. ...
We consider the problem of constructing a bounded-degree planar geometric spanner for a unit disk graph modeling a wireless network. The related problem of constructing a planar geometric spanner of a Euclidean graph has been extensively studied in the literature. It is well known that the Delaunay subgraph is a planar geometric spanner with stretch factor ¢ ¤ £ ¦ © ; however, its degree may not be bounded. Significant work has been done on developing algorithms for constructing bounded-degree planar geometric spanners of Euclidean graphs. Our first result presents a very simple linear time algorithm for constructing a subgraph of the Delaunay graph with stretch factor ¤ " ! # $ & %' & (0) 1 3 2 4 5 ¦ 6 & 7 and de-gree bounded by ' , for any integer parameter ' 9 8 @ . This result immediately implies an algorithm for constructing a planar geometric spanner of a Euclidean graph with stretch factor B A C ¢ ¤ £ ¦ and degree bounded by ' , for any integer parameter ' D 8 @ . Our second contribution lies in developing the structural results necessary to transfer our analysis and algorithm from Euclidean graphs to unit disk graphs. We obtain a very simple strictly-localized algorithm that, given a unit disk graph embedded in the plane, constructs a planar geometric spanner with the above stretch factor and degree bound. The two results dramatically improve the previous results in all aspects, as shown in the paper.
We study spanning properties of sparse cone-based graphs of constant degree, parameterized by a positive integer . Cone-based graphs partition the space around each vertex into k equiangular cones, and select at most one outgoing edge in each cone. This guarantees an out-degree of at most k, but the in-degree may be unbounded. To bound the in-degree, at most one incoming edge is retained in each cone. This yields a sparse graph of degree at most 2k (in-degree k and out-degree k). In this paper we introduce the notion of canonical k-cone graphs and establish a spanning ratio of 16.76 for this class of graphs, provided that and . The spanning ratio decreases to 4.64 as increases to 8. We show that both Yao-Yao and Theta-Theta graphs are canonical k-cone graphs and therefore they inherit these spanning ratios. Yao-Yao and Theta-Theta graphs differ only in the way edges are selected. Yao-Yao graphs select an edge of minimum Euclidean length, whereas Theta-Theta graphs select an edge of minimum orthogonal projection onto the cone bisector.
Spanner construction is one of the most important techniques for topology control in wireless networks. A spanner can help not only to decrease the number of links and to maintain connectivity but also to ensure that the distance between any pair of communication nodes is within some constant factor from the shortest possible distance. Due to the non-locality, constructing a spanner is especially challenging under the physical interference model signal-to-interference-and-noise-ratio (SINR). In this paper, we develop two localized randomized algorithms SINR-directed-YG and SINR-undirected-YG to construct a directed Yao graph (YG) and an undirected YG in O(log n) (n is the number of wireless nodes) time slots with a high probability, in which each node is capable of performing successful local broadcasts to gather neighborhood information within a certain region and the SINR constraint is satisfied at all the steps of the algorithms. The resultant graph of SINR-undirected-YG, which is based on SINR-directed-YG, possesses a constant stretch factor 1/1-2\sin(π/c), where c > 6 is a constant. To the best of our knowledge, SINR-undirected-YG is the first spanner construction algorithm under SINR. We also obtain Yao-Yao graph under SINR. Extensive theoretical performance analysis and simulation study are carried out to verify the effectiveness and the efficiency of our proposed algorithms.
We present a local distributed algorithm that, given a wireless ad hoc network modeled as a unit disk graph U in the plane, constructs a planar power spanner of U whose degree is bounded by k and whose stretch factor is bounded by 1 + (2sin pi/k)<sup>p</sup>, where k ges 10 is an integer parameter and p isin [2, 5] is the power exponent constant. For the same degree bound k, the stretch factor of our algorithm significantly improves the previous best bounds by Song et al. We show that this bound is near-optimal by proving that the slightly smaller stretch factor of 1 + (2sin pi/k+1)<sup>p</sup> is unattainable for the same degree bound k. In contrast to previous algorithms for the problem, the presented algorithm is local. As a consequence, the algorithm is highly scalable and robust. Finally, while the algorithm is efficient and easy to implement in practice, it relies on deep insights on the geometry of unit disk graphs and novel techniques that are of independent interest.
We present a strictly-localized distributed algorithm that, given a wireless ad-hoc network modeled as a unit disk graph in the plane, constructs a planar power spanner of whose degree is bounded by and whose stretch factor is bounded by , where is an integer parameter and is the power exponent constant. For the same degree bound , the stretch factor of our algorithm significantly improves the previous best bounds by Song et al. and Kanj and Perkovi´ c. We show that this bound is near-optimal by proving that the slightly smaller stretch factor of is unattainable for the same degree bound . In contrast to previous algorithms by Song et al. and by Kanj and Perkovic, the presented algorithm is strictly localized: the construction of the power spanner depends solely on the local structure and does not require information propagation. As a consequence, the algorithm is highly scalable and robust. Moreover, on a graph with points and edges the algorithm exchanges no more than messages and has a local processing time of
