Coordinating Boundaries: Improved Approximation Algorithms for Unweighted Non-Preemptive Throughput Maximization
Weitian Tong, Yao Xu
We study unweighted nonpreemptive throughput maximization: given jobs with processing times, release times, and deadlines, schedule a maximum-cardinality subset on identical machines. For every fixed $\varepsilon>0$, we give randomized algorithms with expected approximation ratios $17/13+\varepsilon$ in polynomial time and $21/17+\varepsilon$ in pseudopolynomial time. These improve the respective $4/3+\varepsilon$ and $5/4+\varepsilon$ guarantees of Armbruster, Grandoni, Tinguely, and Wiese [STOC'26]. Both results hold for an arbitrary number of identical machines. Our algorithms build on their configuration-LP and matching framework, which partitions time into blocks. For a job whose window meets multiple blocks, its boundary blocks are the first and last such blocks. Crossing boundary pairs, whose endpoints strictly interleave, permit additional assignments to sampled execution slots, while a noncrossing family can be coordinated using consistent joint distributions on at most three blocks. The exchange analysis accounts for fractional job assignments that must be erased before inserting an additional job. For the pseudopolynomial implementation, we project configurations onto selected job identities and use separate configuration distributions with common placement marginals. This retains efficient pricing while enforcing the correlations needed for coordination.
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