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Hash-based Proof-of-Work (PoW) used in the Bitcoin Blockchain leads to highenergy consumption and resource wastage. In this paper, we aim to re-purposethe energy by replacing the hash function with real-life problems havingcommercial utility. We propose Chrisimos, a useful Proof-of-Work where minersare required to find a minimal dominating set for real-life graph instances. Aminer who is able to output the smallest dominating set for the given graphwithin the block interval time wins the mining game. We also propose a newchain selection rule that ensures the security of the scheme. Thus our protocolalso realizes a decentralized minimal dominating set solver for any graphinstance. We provide formal proof of correctness and show via experimentalresults that the block interval time is within feasible bounds of hash-basedPoW.

Chrisimos: A useful Proof-of-Work for finding Minimal Dominating Set of a graph