Learn to Optimize the Constrained Shortest Path on Large Dynamic Graphs

Abstract

The constrained shortest path ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {CSP}$</tex-math></inline-formula> ) problem has wide applications in travel path planning, mobile video broadcasting and network routing. Existing works do not work well on large dynamic graphs and suffer from either ineffectiveness or low scalability issues. To overcome these issues, in this paper, we propose an efficient and effective solution framework, namely <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {CSP\_{G}S}$</tex-math></inline-formula> . The solution framework includes two key components: (1) the techniques to decompose a large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {CSP}$</tex-math></inline-formula> instance into multiple small sub-instances and (2) the developed learning model <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {CSP\_{D}QN}$</tex-math></inline-formula> to solve small <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {CSP}$</tex-math></inline-formula> instances. The evaluation result on real road network graphs indicates that our approach <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {CSP\_{G}S}$</tex-math></inline-formula> performs well on large dynamic graphs by rather high quality and reasonable running time, and particularly adapt to significant graph changes even with broken edges. To the best of our knowledge, this is the first learning-based model to well solve the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {CSP}$</tex-math></inline-formula> problem on large dynamic graphs.