Existing standards for player characterisation in tokenised state machine replication protocols depend on honest players who will always follow the protocol, regardless of possible token increases for deviating. Given the ever-increasing market capitalisation of these tokenised protocols, honesty is becoming more expensive and more unrealistic. As such, this out-dated player characterisation must be removed to provide true guarantees of safety and liveness in a major stride towards universal trust in state machine replication protocols and a new scale of adoption. As all current state machine replication protocols are built on these legacy standards, it is imperative that a new player model is identified and utilised to reflect the true nature of players in tokenised protocols, now and into the future.

We present Min-Rounds BC (MRBC), a distributed-memory algorithm in the CONGEST model that computes the betweenness centrality (BC) of every vertex in a directed unweighted n-node graph in O(n) rounds. Min-Rounds BC also computes all-pairs-shortest-paths (APSP) in such graphs. It improves the number of rounds by at least a constant factor over previous results for unweighted directed APSP and for unweighted BC, both directed and undirected.

We present a deterministic distributed algorithm to compute all-pairs shortest paths (APSP) in an edge-weighted directed or undirected graph. Our algorithm runs in Õ (n^3/2 ) rounds in the Congest model, where n is the number of nodes in the graph. This is the first o(n^2) rounds deterministic distributed algorithm for the weighted APSP problem. Our algorithm is fairly simple and incorporates a deterministic distributed algorithm we develop for computing a 'blocker set' [King99], which has been used earlier in sequential dynamic computation of APSP.