Abstract
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. 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. We then extend this algorithm to run on the k-channel BCM. For any small fixed ε > 0, our list ranking algorithm runs in O(n/k) time slots with no station being awake for more than O(1) time slots, provided that k ≤ n 1 − ge. Clearly, Ω(n/k) 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.
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Nakano, K. (2002). Time and Energy Optimal List Ranking Algorithms on the k-Channel Broadcast Communication Model. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_30
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DOI: https://doi.org/10.1007/3-540-45655-4_30
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