TL;DR: This work forms this multicast problem and proves that linear coding suffices to achieve the optimum, which is the max-flow from the source to each receiving node.
Abstract: Consider a communication network in which certain source nodes multicast information to other nodes on the network in the multihop fashion where every node can pass on any of its received data to others. We are interested in how fast each node can receive the complete information, or equivalently, what the information rate arriving at each node is. Allowing a node to encode its received data before passing it on, the question involves optimization of the multicast mechanisms at the nodes. Among the simplest coding schemes is linear coding, which regards a block of data as a vector over a certain base field and allows a node to apply a linear transformation to a vector before passing it on. We formulate this multicast problem and prove that linear coding suffices to achieve the optimum, which is the max-flow from the source to each receiving node.
TL;DR: It is shown that if n nodes are placed in a disc of unit area in !
Abstract: In wireless data networks each transmitter’s power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In particular, if the nodes in the network are assumed to cooperate in routing each others’ packets, as is the case in ad hoc wireless networks, each node should transmit with just enough power to guarantee connectivity in the network. Towards this end, we derive the critical power a node in the network needs to transmit in order to ensure that the network is connected with probability one as the number of nodes in the network goes to infinity. It is shown that if n nodes are placed in a disc of unit area in ℜ2 and each node transmits at a power level so as to cover an area of πr 2 = (log n + c(n))/n, then the resulting network is asymptotically connected with probability one if and only if c(n) → +∞.
TL;DR: In this paper, the authors present an algorithm for routing in wireless ad hoc networks using information about the geographical location of the nodes, where each node knows its geographical position and the position of the node to which it wants to send a packet.
Abstract: We present an algorithm for routing in wireless ad hoc networks using information about the geographical location of the nodes. We assume each node knows its geographical position and the position of the node to which it wants to send a packet. Initially, the nodes know only their neighbors. But over time they discover other nodes in the network. The routing table at a node S is a list , where p/sub i/ is a geographical position and S/sub i/ is a neighbor of node S. When node S receives a packet for a node D at position pos(D), it finds the p/sub i/ in its routing table which is closest to pos(D) and forwards the packet to the neighbor S/sub i/. We prove the correctness of the algorithm and show that our algorithm naturally aggregates the nodes so that the routing tables remain small. We show that the mean routing table size is O(L~logn), where L~ is the average number of hops between two nodes and n is the number of nodes in the network. We also present methods for taking positional errors, node failures and mobility into account. We justify the results through simulation.
TL;DR: This paper formulate the relay node placement in wireless sensor networks as two optimization problems: (i) Connected Relay Node Single Cover (CRNSC) problem and (ii) 2-Connected Relays Node Double Cover (2CRNDC) problem, and presents two polynomial time approximation algorithms to solve the CRNSC problem.
TL;DR: In this paper, an amorphous communication network having no traditional wireless backbone has plural roving or migratory access node (200) or terminal devices that are carried or transported along with individuals.
Abstract: An amorphous communication network having no traditional wireless backbone has plural roving or migratory access node (200) or terminal devices that are carried or transported along with individuals. Each wireless node (200) has a user interface and a local ID, e.g., an IP address, URL, telephone number. Voice, data, or video is transferred to other migratory nodes (104) or to a conventional land-based telephone or data terminal via a PSTN, Internet, ATM network, etc. A geolocation detector in the node (200), such as a GPS, keeps track of the instantaneous position, which is conveyed to a locally or remotely stored database (400). A local processor (250) accesses this database (400) to determine node-to-node paths to a destination when the node (200) operates as a source. A node (200) captures a transmitted message when the destination address in the message matches its local address, or otherwise forwards the message towards a destination if the address does not match. Acknowledgements are sent between nodes (104) upon successful receipt of information. The node's wireless transceiver (260) also adapts to the environment and terrain to control transmission and reception characteristics according to bandwidth, inter-node spacing, signal strength, bit error rate, node population density, frequency spectrum, data rate and/or air interface protocol. Nodes (200) may periodically or randomly unicast or broadcast its ID and/or position data to update a database (400), which then may be propagated to other databases throughout the network. A database (400) may reside locally within a node (200) or at fixed regional locations (106) that are linked together to form a global database.