Distributed Algorithms for TDMA Link Scheduling in Sensor Networks
International Journal of Networking and Computing
The paper is devoted to Time Division Multiple Access Link Scheduling Protocols in wireless sensor networks for full duplex (two-way) communication, where each sensor is scheduled on an incident link as a transmitter and as a receiver in two different time slots. We formulate the full duplex link scheduling problem (FDLSP) as distance-2 edge coloring in bi-directed graphs and prove tighter lower and upper bounds for the FDLSP problem. We formulate the FDLSP problem as an integer linear program
... ILP). Then, we present two ∆-approximation distributed algorithms for growth bounded graphs (GBG), for modeling the sensor networks, and for general graphs, ∆ being the maximum node degree in the network. The first algorithm is a synchronous ∆-approximation algorithm based on finding maximal independent sets. The second is an asynchronous ∆-approximation depth first search (DFS) based algorithm. The maximal independent set based algorithm requires only O(∆log * n) communication rounds (where n is the number of processors in the network) in growth bounded graphs. For general graphs, the maximal independent set based algorithm requires O(∆ 4 + ∆ 3 log * n) communication rounds, improving upon the previous best known algorithm with O(n∆ 2 + n 2 m) communication rounds (where m is the number of links in the network). The asynchronous DFS based algorithm requires only O(n) communication rounds for both general and growth bounded graphs. The simulations show that the proposed algorithms assign on average equal or fewer number of time slots compared to the best known distributed algorithm while being significantly faster. International Journal of Networking and Computing sensors networks. In unit disk graphs, the sensors are points in the Euclidean plane and two sensors are neighbors (share a link) if their Euclidean distance is less than or equal to 1. This implies that sensors have identical transmission range. But, this does not reflect the reality since there are factors such as mobility and available battery power which affect the transmission range of the sensors. Thus, recently, new geometrical models have been studied in sensors network community that better model sensor networks in realty. These models include quasi unit disk graphs and unit ball graphs. Such models capture more realistic scenarios concerning connectivity based on distance  . All of the aforementioned models are members of a larger graph family called growth bounded graphs (GBG)  . Growth bounded graphs assume only a limit on the number of independent nodes in a neighborhood (an independent node is a node that all of its neighbors are not independent). More formally, a graph G is growth bounded if there is a polynomially bounding function f (r), such that the number of independent nodes that are at shortest distance r from a node is given by f (r)  . In this paper, we model and analyze the sensor network as growth bounded graphs. We use UDG for our experiments, because it is not known how to generate GBG in practice, while theoretical analysis of the algorithms remains valid for UDG. Communication Model. In this paper, we develop algorithms for two distributed communication models, namely synchronous and asynchronous message passing models. In both models, the communication network is modeled as an undirected graph (V, E), where the set of nodes V represents processors of the network and the set of links E represents bidirectional non-interfering communication channels, where we assume the existence of a protocol to carry out the communication among the nodes in the network correctly. Each node has a distinct identity. In a single round a node carries out some computations, sends message to its neighbors and receives messages from of its neighbors. In the synchronous message passing model for distributed computing [5, 11] , each node sends/receives to/from all of its neighbors in every communication round, and the communication rounds are synchronized. If we assume that each round takes one time unit, then the time complexity of the algorithm is the number of time units taken from start to completion. In the asynchronous message passing model for distributed computing, communication rounds are not synchronized, i.e., the time complexity of algorithm is the worst-case number of time units from start to completion  . Contribution. In this paper, our contribution includes the following: Formulating FDLSP as distance-2 edge coloring in bi-directed graphs. Proving a new lower bound for the number of time slots required for FDLSP, which is max(2(δ+largest cluster size+ no.of edges in largest joint clique size)) that is tighter than previous lower bound of 2∆, ∆ being the maximum node degree in the network and δ being a given node degree. Proving an upper bound on the number of time slots, which is 2∆ 2 , and the existence of ∆-approximation algorithm for the FDLSP problem. Problem formulation of FDLSP as an integer linear program. A synchronous ∆-approximation distributed maximal independent set based fast algorithm for FDLSP, which requires O(∆log * n) communication rounds in growth bounded graphs, ∆ being the maximum node degree, and O(∆ 4 + ∆ 3 log * n) communication rounds in general graphs, compared to the best known algorithm for FDLSP problem which requires O(n 2 m + nm∆) communication rounds. An asynchronous ∆-approximation distributed DFS-based algorithm for FDLSP which improves the communication rounds from previous a previous algorithm  with O(n 2 m + nm∆) communication rounds to O(n) and reduces the average number of time slots in practice. Implementation and experimental comparison with a distributed edge coloring algorithm from  showing the same number of time slots on average for the maximal independent set based algorithm while significantly reducing the communication complexity.