Local search

Thu, 19 Mar 2026 19:04:21 +0100

Local search is a simple approximation algorithm, which doesn’t necessarirly lead to the best result, instead it has a tendency to get stuck in a local minimum. Still if combined with other techniques like for example use of heuristics it can cheaply with low overhead improve the quality of the found solution.

pseudocode:

function local_search:
INPUT: graph of the state G = (V,E), cost function f
OUTPUT: found state

s <- generate_initial_state()

while (true): // we might want iteration amount limit in case the state space is infinite and the optimum unreachable
 s' <- s
 for n in get_neighbors(s):
 if f(n) < f(s'):
 s' <- n
 if (s' /= s):
 s <- s'
 else:
 break
return s

This pseudocode was written for a graph but can easily be generalized to any general solution space. Simply instead of looking at neighbours of a state we at states we can possibly “go to”.

Minimum Spanning Tree

Wed, 18 Mar 2026 16:25:43 +0100

Here we’re going to cover what are Minimum Spanning Trees (MSTs), methods for finding them and use cases.

What is a tree?
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In graph theory we call graph $T=(V,E)$ a tree if it is connected and it doesn’t have any cycles.

Forrest

We call a graph with no cycles a forrest (contrary to the tree it doesn’t need to be connected). In a forrest each connected component is a tree.

Algorithms on JinerX blog

Local search

Minimum Spanning Tree

What is a tree? #

What is a tree?
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