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Commit a958ac88 authored by Jakub Janák's avatar Jakub Janák
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...@@ -15,12 +15,12 @@ what is the shortest possible route that visits each city exactly once and retur ...@@ -15,12 +15,12 @@ what is the shortest possible route that visits each city exactly once and retur
It is not particularly hard to define the problem, but it is tough to solve it effectively (maybe even impossible). It is not particularly hard to define the problem, but it is tough to solve it effectively (maybe even impossible).
The mathematical definition would be: The mathematical definition would be:
Given a directed, weighted graph \( G = (N, E) \), where: Given a directed, weighted graph $G = (N, E)$, where:
\( N = \{v_1, v_2, \dots, v_n\} \) is a set of nodes, $N = \{v_1, v_2, \dots, v_n\} $ is a set of nodes,
\( E = \{e_1, e_2, \dots, e_n\} \) is a set of edges, $E = \{e_1, e_2, \dots, e_n\} $ is a set of edges,
\( w: E \to \mathbb{R}^+ \) is a weight function, returning the weight of an edge. $w: E \to \mathbb{R}^+ $ is a weight function, returning the weight of an edge.
The goal is to find a Hamiltonian cycle \( H \subseteq E \) such that: The goal is to find a Hamiltonian cycle $H \subseteq E$ such that:
1. Each node in \( N \) is visited exactly once, and at the end returns to the starting node. 1. Each node in \( N \) is visited exactly once, and at the end returns to the starting node.
2. The total weight of \( H \) is minimal. 2. The total weight of \( H \) is minimal.
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