Faster algorithms for bicriteria scheduling of identical jobs on uniform machines

<p style='text-indent:20px;'>This paper studies the problem of scheduling <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> jobs with equal processing times on id="M2">\begin{document}$ m uniform machines to optimize two criteria simultaneously. The main contribution is an id="M3">\begin{document}$ O(n\log m+n^3) $\end{document}</tex-math></inline-formula>-time algorithm for general min-max criteria, improving previous id="M4">\begin{document}$ m+n^4) time complexity. For a particular min-sum criterion (total weighted completion or total tardiness) in combination criterion, id="M5">\begin{document}$ algorithms are also obtained, id="M6">\begin{document}$ m+n^3\log n) can produce all Pareto optimal points together corresponding schedules.</p>