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01234 012345 (a) First mining round ρ12. (b) Second mining round ρ2. Fig. 2: Illustrating the mining process of Green-PoW in one epoch of time (τ2). The blue node is the winner of the first round (ω2) and generates the block number 4 (blue square). Red nodes are losing participants in the mining. The dashed blue nodes are second place winners (M2), which will be the only nodes to handle the block in the next round (ρ2). The green node is the winner of the second round which generates block number 5 (green square). Gray nodes are idle miners that do not participate in the mining during the second round {M \ M2}. 4.1 Runner(s)-up Election In the original PoW, when a puzzle-related block is solved by some miner, all the other network nodes desist the mining of that block and immediately start mining the next block. In Green-PoW, if a valid block is found and the first place winner is elected, the race will continue between miners to also determine the runner-up, i.e., the node that has the second place in the same block race. We denote by ωi the first place winner, and ri the runner-up. Such runner-up (r ) will be the only eligible node to mine in ρ2, and all the ii2 other nodes enter in mining-save mode until the end of ρi . As illustrated in Fig. 3, when a miner mj receives a block from the first place winner it continues the mining of the same block. Miner mj either (1) finds the nonce before receiving a block from another miner claiming the second place; in this case node mj will broadcast an announcement to the entire network that it is the runner-up, and then immediately starts the mining of the next block, or (2) receives a block from another node mk and subsequently, adds it to its runners- up list (M2i ) and then enters the mining-save mode for one round. M2i serves in the second round to make sure that any received block is originated from a valid runner-up. Because of the distributed and asynchronous nature of the network, it is possible to have multiple nodes that consider themselves as runners-up when they find the block at nearly the same time. A similar situation can happen for the first place winner and leads to network fork that is solved later by the longest chain rule [19]. For the runner- up election, this situation will not cause any problem as any node that successfully mines the block in the first round will be considered as a potential runner-up and can participate in the mining race during ρ2i . In this case, the set of multiple runners-up M2i = {ri1 , ri2 , ..., ril }. It is worth noting that having multiple nodes as second-place winners does not affect the system inconsistency, but on the contrary, it improves system liveness as it increases the chance that a block gets mined during the second round. Fig. 3 illustrates a simplified case where a miner will automatically switch to mining-save mode if it receives a block from another node claiming the second place. Algo- rithm 1 also summarizes the different steps of Green-PoW consensus algorithm executed by nodes during mining. As illustrated in Fig. 3 and Algorithm 1, a miner can be in one of the following four mining states; 1) mining a block to win the first place in ρ1, (2) continuing mining a block to win the second place in ρ1, (3) mining a block to win the first place in ρ2 , or (4) mining-save mode. In order to engage a sufficient number of participants in ρ2i and improve the system liveness, in Green-PoW, even if one node has already claimed to be a runner-up, the other nodes can still continue mining. The decision of a node to continue mining the first round’s block depends on the probability of winning the race in ρ2i . A miner that solves the first round’s block very late, will have a very small chance to win as the others have started the mining earlier. For the sake of simplicity, when a node receives the first announcement of a runner-up, it continues mining for only a very short period of time η with the hope of quickly finding the nonce and joining ρ2i . The value of η is subject to liveness and energy trade-off and is expected to be determined based on the rate of block generation in the network. In the next section, we will introduce another liveness parameter and will elaborate more on how η could be tuned. 4.2 Second Round Timeout Since only nodes that successfully mine the first round block may be part of M2i , the number of potential miners in ρ2i , i.e., |M2i |, is naturally limited. While this is advantageous from an energy conservation point of view, it is possible that the system goes to a deadlock and the next block does not get generated. This can happen for instance if miners in M2i are isolated from the rest of the network, inadvertent in case of network segmentation, or intentionally by an adversary who launches an eclipse attack [21]. To mitigate this problem and ensure system liveness, Green-PoW employs a time-out at the beginning of each ρ2i . The time-out should be greater than the average time needed to generate a new block. If a block announcement is not received before the time-out, inactive nodes quit the mining-save mode and start immedi- ately ρ2i . However, because of the asynchronous nature of the network and the malicious behavior of some nodes, the introduction of time-out may lead to some special cases that we discuss in the following: 5PDF Image | Efficient Blockchain Proof-of-Work Consensus Algorithm
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