This paper proposes a memory-efficient algorithm of variable-size all-to-all communication based on bitonic sort and in-place merge. The algorithm takes O(N log2 P) computation and communication time and requires merely O(P) extra space for the communication among P processes having N elements of data to be exchanged for each. We also discuss another algorithm which takes O(MP log P) time where M is the size of the largest chunk which a process must send to another process and thus is expected to be O(N/P) in most practical applications to make the time complexity O(N log P). We implemented the first sort-based algorithm to show it works with reasonable efficiency.This paper proposes a memory-efficient algorithm of variable-size all-to-all communication based on bitonic sort and in-place merge. The algorithm takes O(N log2 P) computation and communication time and requires merely O(P) extra space for the communication among P processes having N elements of data to be exchanged for each. We also discuss another algorithm which takes O(MP log P) time where M is the size of the largest chunk which a process must send to another process and thus is expected to be O(N/P) in most practical applications to make the time complexity O(N log P). We implemented the first sort-based algorithm to show it works with reasonable efficiency.