Using Dijkstra’s algorithm to compute the shortest paths in a graph from a single source node to all other nodes is common practice in industry and academia. Although the original description of the algorithm advises using a Fibonacci Heap as its internal queue, it has been noted that in practice, a binary (or d-ary) heap implementation is significantly faster. This paper introduces an even fas...

The notion of self-stabilization was rst introduced by Dijkstra : it is the property for a system to eventually recover itself a legitimate state after any perturbation modifying the memory state. This paper proposes a self-stabilizing depth-rst token circulation protocol for uniform rooted networks. Such an algorithm is very convenient to obtain the mutual exclusion or to construct a spanning ...

In 1985 Fischer, Lynch, and Paterson (FLP) proved that consensus is not attainable in asynchronous message passing systems with failures. In the following years, Loui and Abu-Amara, and Herlihy proved that solving consensus in an asynchronous shared memory system is harder than implementing a read/write register. However, it was not known whether read/ write registers are implementable in async...

We study the impact of using different priority queues in the performance of Dijkstra’s SSSP algorithm. We consider only general priority queues that can handle any type of keys (integer, floating point, etc.); the only exception is that we use as a benchmark the DIMACS Challenge SSSP code [1] which can handle only integer values for distances. Our experiments were focussed on the following: 1....

We study zero-sum dynamic games with deterministic transitions and alternating moves of the players. Player 1 aims at reaching a terminal set and minimising a running and final cost. We propose and analyse an algorithm that computes the value function of these games extending Dijkstra’s algorithm for shortest paths on graphs. We also show the connection of these games with numerical schemes for...

The Hoare state monad provides a powerful means of structuring the verification of higher-order, stateful programs. This paper defines a new variant of the Hoare state monad, which, rather than being a triple of a pre-condition, a return type, and a post-condition, is a pair of a return type and a predicate transformer. We dub this monad the Dijkstra state monad. Using the Dijkstra state monad,...