Scheduling lower bounds via AND subset sum.

Amir Abboud, Karl Bringmann, Danny Hermelin, Dvir Shabtay

Research output: Contribution to journalArticlepeer-review

Abstract

Given N instances of Subset Sum, the AND Subset Sum problem asks to determine whether all of these instances are yes-instances; that is, whether each set of integers has a subset that sums up to the target integer . We prove that this problem cannot be solved in time , for and any , assuming the ∀∃ Strong Exponential Time Hypothesis (∀∃-SETH). We then use this result to exclude -time algorithms for several scheduling problems on n jobs with maximum processing time , assuming ∀∃-SETH. These include classical problems such as , the problem of minimizing the total weight of tardy jobs on a single machine, and , the problem of minimizing the number of tardy jobs on two identical parallel machines.
Original languageEnglish
Pages (from-to)29-40
Number of pages12
JournalJournal of Computer and System Sciences
Volume127
DOIs
StatePublished - 2022

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