Space and Step Complexity Efficient Adaptive Collect

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Space and step complexity efficient deterministic adaptive to total contention collect algorithms are presented. One of them has an optimal O(k) step and O(n) space complexities, but restrict the processes identifiers size to O(n). Where n is the total number of processes in the system and k is the total contention, the total number of processes active during the execution. Unrestricting the name space increases the space complexity to O(n 2) leaving the step complexity at O(k). To date all deterministic adaptive collect algorithms that we are aware of are either nearly quadratic in their step complexity or their memory overhead is exponential in n.