Hash-based Proof-of-Work (PoW) used in the Bitcoin Blockchain leads to high energy consumption and resource wastage. In this paper, we aim to re-purpose the energy by replacing the hash function with real-life problems having commercial utility. We propose Chrisimos, a useful Proof-of-Work where miners are required to find a minimal dominating set for real-life graph instances. A miner who is able to output the smallest dominating set for the given graph within the block interval time wins the mining game. We also propose a new chain selection rule that ensures the security of the scheme. Thus our protocol also realizes a decentralized minimal dominating set solver for any graph instance. We provide formal proof of correctness and show via experimental results that the block interval time is within feasible bounds of hash-based PoW.

翻译：基于哈希的工作量证明（PoW）在比特币区块链中导致高能耗和资源浪费。本文旨在通过将哈希函数替换为具有商业实用性的现实问题，重新利用这些能源。我们提出Chrisimos，一种有用的工作量证明机制，其中矿工需针对现实图实例寻找最小支配集。能够在区块间隔时间内输出给定图的最小支配集的矿工赢得挖矿竞赛。我们还提出一种新的链选择规则，确保方案的安全性。因此，我们的协议也为任何图实例实现了一个去中心化的最小支配集求解器。我们提供了正确性的形式化证明，并通过实验结果表明，区块间隔时间在基于哈希的PoW的可行范围内。