7286364
Capacity bounds for ad hoc and hybrid wireless networks
We study the capacity of static wireless networks, both ad hoc and hybrid, under the Protocol and Physical Models of communication, proposed in [1]. For ad hoc networks with <i>n</i> nodes, we show that under the Physical Model, where signal power is assumed to attenuate as 1/r<sup>α</sup>, α > 2, the transport capacity scales as Θ(√<i>n</i>) bit-meters/sec. The same bound holds even when the nodes are allowed to approach arbitrarily close to each other and even under a more generalized notion of the Physical Model wherein the data rate is Shannon's logarithmic function of the SINR at the receiver. This result is sharp since it closes the gap that existed between the previous best known upper bound of O(<i>n</i><sup>α-1/α</sup>) and lower bound of Ω(√n).
 We also show that any spatio-temporal scheduling of transmissions and their ranges that is feasible under the Protocol Model can also be realized under the Physical Model by an appropriate choice of power levels for appropriate thresholds. This allows the generalization of various lower bound constructions from the Protocol Model to the Physical Model. In particular, this provides a better lower bound on the best case transport capacity than in [1].
 For hybrid networks, we consider an overlay of μ<i>n</i> randomly placed wired base stations. It has previously been shown in [6] that if all nodes adopt a common power level, then each node can be provided a throughput of at most Θ(1/log <i>n</i>) to randomly chosen destinations. Here we show that by allowing nodes to perform power control and properly choosing ν(1/log <i>n</i>), it is further possible to provide a throughput of Θ(1) to any fraction <i>f</i>, 0 < <i>f</i> < 1, of nodes. This result holds under both the Protocol and Physical models of communication. On the one hand, it shows that that the aggregate throughput capacity, measured as the sum of individual throughputs, can scale linearly in the number of nodes. On the other hand, the result underscores the importance of choosing minimum power levels for communication and suggests that simply communicating with the closest node or base station could yield good capacity even for multihop hybrid wireless networks.
8476709
On the /spl theta/-coverage and connectivity of large random networks
Wireless planar networks have been used to model wireless networks in a tradition that dates back to 1961 to the work of E. N. Gilbert. Indeed, the study of connected components in wireless networks was the motivation for his pioneering work that spawned the modern field of continuum percolation theory. Given that node locations in wireless networks are not known, random planar modeling can be used to provide preliminary assessments of important quantities such as range, number of neighbors, power consumption, and connectivity, and issues such as spatial reuse and capacity. In this paper, the problem of connectivity based on nearest neighbors is addressed. The exact threshold function for /spl theta/-coverage is found for wireless networks modeled as n points uniformly distributed in a unit square, with every node connecting to its /spl phi//sub n/ nearest neighbors. A network is called /spl theta/-covered if every node, except those near the boundary, can find one of its /spl phi//sub n/ nearest neighbors in any sector of angle /spl theta/. For all /spl theta//spl isin/(0,2/spl pi/), if /spl phi//sub n/=(1+/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, it is shown that the probability of /spl theta/-coverage goes to one as n goes to infinity, for any /spl delta/>0; on the other hand, if /spl phi//sub n/=(1-/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, the probability of /spl theta/-coverage goes to zero. This sharp characterization of /spl theta/-coverage is used to show, via further geometric arguments, that the network will be connected with probability approaching one if /spl phi//sub n/=(1+/spl delta/)log/sub 2/n. Connections between these results and the performance analysis of wireless networks, especially for routing and topology control algorithms, are discussed.
2961249
The capacity of wireless networks
When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput /spl lambda/(n) obtainable by each node for a randomly chosen destination is /spl Theta/(W//spl radic/(nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is /spl Theta/(W/spl radic/An) bit-meters per second. Thus even under optimal circumstances, the throughput is only /spl Theta/(W//spl radic/n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance.
63547373
The transport capacity of wireless networks over fading channels
We study the transport capacity of wireless networks with fading, in the high attenuation regime where either the medium is absorptive or the path loss exponent is greater than 3. For a network of n nodes we show that even were the states of all channels to be noncausally known a-priori, the transport capacity is no more than O(n). On the other hand, even when the channels are frequency selective and independent from time to time, G(n) is achievable through a multihop strategy
6349082
The Number of Neighbors Needed for Connectivity of Wireless Networks
Unlike wired networks, wireless networks do not come with links. Rather, links have to be fashioned out of the ether by nodes choosing neighbors to connect to. Moreover the location of the nodes may be random.The question that we resolve is: How many neighbors should each node be connected to in order that the overall network is connected in a multi-hop fashion? We show that in a network with n randomly placed nodes, each node should be connected to Θ(log n) nearest neighbors. If each node is connected to less than 0.074log n nearest neighbors then the network is asymptotically disconnected with probability one as n increases, while if each node is connected to more than 5.1774log n nearest neighbors then the network is asymptotically connected with probability approaching one as n increases. It appears that the critical constant may be close to one, but that remains an open problem.These results should be contrasted with some works in the 1970s and 1980s which suggested that the “magic number” of nearest neighbors should be six or eight.
8759627
SEEDEX: a MAC protocol for ad hoc networks
Motivated by the poor experimental scaling reported in a study of the performance of ad hoc networks in [15], we propose a new protocol for media access control in ad hoc networks. Our protocol seeks to avoid collisions without making explicit reservations for each and every packet. The key idea is to employ a random schedule which is driven by a pseudo-random number generator. By exchangine the seeds of their pseudo-random number generators within two-hop neighborhood, the nodes effectively publish their schedules to all hidden as well as exposed nodes. This allows each node to opportunistically choose transmission slots. This scheme can also be employed during the reservation phase of a protocol such as IEEE 802.11. Throughput calculations and simulation results are presented
7212084
Finding large sticks and potatoes in polygons
We study a class of optimization problems in polygons that seek to compute the "largest" subset of a prescribed type, e.g., a longest line segment ("stick") or a maximum-area triangle or convex body ("potato"). Exact polynomial-time algorithms are known for some of these problems, but their time bounds are high (e.g., O(n7) for the largest convex polygon in a simple n-gon). We devise efficient approximation algorithms for these problems. In particular, we give near-linear time algorithms for a (1 - ∈)-approximation of the biggest stick, an O(1)-approximation of the maximum-area convex body, and a (1 - ∈)-approximation of the maximum-area fat triangle or rectangle. In addition, we give efficient methods for computing large ellipses inside a polygon (whose vertices are a dense sampling of a closed smooth curve). Our algorithms include both deterministic and randomized methods, one of which has been implemented (for computing large area ellipses in a well sampled closed smooth curve).
42584661
Minimal Vertex Separators of Chordal Graphs
Chordal graphs form an important and widely studied subclass of perfect graphs. The set of minimal vertex separators constitute an unique class of separators of a chordal graph and capture the structure of the graph. In this paper, we explore the connection between perfect elimination orderings of a chordal graph and its minimal vertex separators. Specifically, we prove a characterization of these separators in terms of the monotone adjacency sets of the vertices of the graph, numbered by the maximum cardinality search (MCS) scheme. This leads to a simple linear-time algorithm to identify the minimal vertex separators of a chordal graph using the MCS scheme. We also introduce the notion of multiplicity of a minimal vertex separator which indicates the number of different pairs of vertices separated by it. We prove a useful property of the lexicographic breadth first scheme (LBFS) that enables us to determine the multiplicities of minimal vertex separators of a chordal graph.
150407
Infrastructure for the quantum internet
A team of researchers from the Massachusetts Institute of Technology (MIT) and Northwestern University (NU) is developing a system for long-distance, high- delity qubit tele-portation. Such a system will be required if future quantum computers are to be linked together into a quantum Internet. This paper presents recent progress that the MIT/NU team has made, beginning with a review of the teleportation architecture and its loss-limited performance analysis.
7166264
Minimal Tail-Biting Trellises for Certain Cyclic Block Codes Are Easy to Construct
We give simple algorithms for the construction of generator matrices for minimal tail-biting trellises for a powerful and practical subclass of the linear cyclic codes, from which the combinatorial representation in the form of a graph can be obtained by standard procedures.
15224609
Codes for Optical CDMA
There has been a recent upsurge of interest in applying Code Division Multiple Access (CDMA) techniques to optical networks. Conventional spreading codes for OCDMA, known as optical orthogonal codes (OOC) spread the signal in the time domain only, which often results in the requirement of a large chip rate. By spreading in both time and wavelength using two-dimensional OOCs, the chip rate can be reduced considerably. This paper presents an overview of 1-D and 2-D optical orthogonal codes as well as some new results relating to bounds on code size and code construction.