A Broadcast Communication Model (BCM, for short) is a distributed system with no central arbiter populated by n processing units referred to as stations. The stations can communicate by broadcasting/receiving a data packet to one of k distinct communication channels. We assume that the stations run on batteries and expend power while broadcasting/receiving a data packet. Thus, the most important measure to evaluate algorithms on the BCM is the number of awake time slots, in which a station is broadcasting/receiving a data packet. The main contribution of this paper is to present time and energy optimal list ranking algorithms on the BCM. We first show that the rank of every node in an n-node linked list can be determined in O(n) time slots with no station being awake for more than O(1) time slots on the single-channel n-station BCM with no collision detection. We then extend this algorithm to run on the k-channel BCM. For any small fixed ∊>0, our list ranking algorithm runs in [Formula: see text] time slots with no station being awake for more than O(1) time slots, provided that k≤n1-∊. Clearly, [Formula: see text] time is necessary to solve the list ranking problem for an n-node linked list on the k-channel BCM. Therefore, our list ranking algorithm on the k-channel BCM is time and energy optimal.
Parallel communicating grammar systems with context-free components are Turing complete for any communication model
