Arpit's Newsletter read by 38000+ engineers
Weekly essays on real-world system design, distributed systems, or a deep dive into some super-clever algorithm.
Determining the shortest path in a distributed system is an important problem to address and it finds its application across multiple use cases like
A key point to consider here is the fact that “shortest” is not only about the distance, but it can also be about the congestion, time, cost of communication lines, cable infra, and much more.
In a distributed network, where nodes are connected via paths/edges having some weight assigned, find the shortest path from a specific source to all the nodes
In this gist, we discuss a synchronous approach which means every node moves forward in the algorithm in sync. There are ways to achieve this, but the implementation of synchronous behavior is out of the scope of this gist.
Because it is a distributed network no node knows the entire topology and weights. They just know
Every node keeps track of dist
which holds the shortest distance to it from the source i0
. Initially, dist
at i0
will be 0
and dist
at all other nodes will be inf
.
At every round, all the nodes will send their dist
across all of their outgoing edges to their neighboring nodes. Every node i
upon receiving an incoming dist
from its immediate neighbor j
compares
dist
dist
+ weight(i, j)
after comparing, if the incoming distance plus the weight of the connecting edge is smaller than its own dist
it means that the distance from i0
to the current node could be shorter and hence, the node updates the parent
suggesting that the shortest path from i0
to i
goes through j
.
After n - 1
rounds, the dist
at every node will contain the shortest distance to it from source i0
, and the parent
will contain one of its immediate neighbors that lies in the shortest path.
We require n - 1
rounds to complete the algorithm, the time complexity of Bellman-Ford Shortest Path in Distributed System is O(n)
. At every round, every node sends dist
message across all of its edges to its immediate neighbors, the communication complexity becomes O(n x |E|)
.
Here's the video ⤵
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Arpit's Newsletter read by 38000+ engineers
Weekly essays on real-world system design, distributed systems, or a deep dive into some super-clever algorithm.