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Sensors 2021, 21, 3822 15 of 32 Table 2. Time and space complexities of algorithms Token Type NFT NFT NFT NFT NFT NFT BulkRead O(n) FT Create O(1) FT ReCreate O(1) FT Bid O(1) FT Transfer O(n) FT ReTransfer O(n) FT Redeem O(1) FT Read O(1) Operation Time Complexity Space Complexity O(1) O(1) O(1) O(1) O(1) O(n) O(1) O(1) O(1) O(n) O(n) O(1) O(1) Create Bid Transfer Redeem Read O(1) O(1) O(1) O(1) O(1) In Hyperledger Fabric, create, update, endorsement policy configurations and deletes are all processed as writes to the state. Thus, NFT Create involves no read operations and two write operations, one to create the token and one to configure the endorsement policy. Also, this operation only uses space to store that one token. The time and space complexities for this algorithm are O(1), as for any invocation, only one token will be created using the mentioned operations. Similarly, NFT Bid (one read, one write), NFT Transfer (one read, three writes) NFT Redeem (one read, one write), NFT Read (one read), FT Create (one read, two writes), FT ReCreate (one read, one write), FT Bid (one read, one write), FT Redeem (one read, one write) and FT Read (one read) will have a constant number of operations as well as space usage for any invocations and thus have both time and space complexities of O(1). NFT BulkRead will execute read operations, which will depend on and grow with the number of tokens owned by the invoking client. Here, each token returned by the range query is considered to be a separate read. Similarly, the space used will also depend on the number of tokens returned. Thus, the time and space complexities of NFT BulkRead are both O(n). FT Transfer and FT ReTransfer will execute one read in order to read the seller’s token. Then, both operations will execute a loop based on the number of bids present. For each bid, they will execute one read to check if the buyer’s token exists and one write to either create (FT Transfer) or update (FT ReTransfer) the buyer’s token. FT Transfer will execute an additional write in order to set the key level endorsement policy for the buyer’s token. In each execution of the loop, both operations will use the space required to operate upon two tokens, the buyer’s token and the seller’s token. As the number of times this loop is run will depend on the number of bids present, the time and space complexities of both FT Transfer and FT ReTransfer are O(n). Finally, at the end of the loop, the seller’s token will be updated with a single write, which is constant for any invocation. Multiple transfers that originate from a single FT perform transfer of value to multiple distinct recipients in a FT Transfer operation. In order to complete comparable transfers in NFT, we would need to perform multiple separate transactions, one for each bid. Thus, even though the time and space complexities of the presented algorithms for FT Transfer and ReTransfer are O(n), we do not consider them to be a bottleneck as they cannot be considered equivalent to a single NFT transfer. A fair comparison, between the value transfer operations Transfer and ReTransfer for FT and Transfer for NFT, should thus consider a single bid per token. We performance test and make a comparison between these three algorithms in Section 4.2. For NFT, retrieving all tokens of a type owned by a client is expected to be a bottleneck if executed on chain. We experimentally investigate this in Section 4.2 and the results of our experiments are shown in Figure 10.PDF Image | Blockchain Based Transaction System with NFT
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