arXiv subjects

Changdao He

Publications and source records attributed to Changdao He.

3 recordsLinked to original sources

arXiv2026

Evaluating SAT Solver Metrics as Predictors of Human-Perceived Nonogram Difficulty

Algorithmic solver effort is often assumed to align with perceived puzzle difficulty, but this assumption is rarely tested against human solving data. We evaluate this assumption for Nonograms, a popular logic puzzle similar to Sudoku in which numeric clues along each row and column determine a unique solution grid. We formulate Nonograms as a constraint satisfaction problem and solve them using existing SAT solvers. We then conduct a user study in which we collect data on both participant interactions and reported difficulty. We find that neither participants' reported difficulty nor their behavioural signals correlate meaningfully with SAT solver metrics; however, we find evidence that expertise moderates the relationship between solver metrics and reported difficulty. In this process, we uncover distinct, recurring solving strategies that indicate human preference for complex propagation, diverging from solver-measured complexity.

cs.HC↗

arXiv2026

Revisiting Real-Time Interval and Throughput Maximization

Job throughput maximization is the central maximization problem in scheduling. Interval scheduling is the special case of throughput maximization when jobs are intervals and therefore there is no slack available in which to schedule a job. It is interesting to know to what extent results for interval scheduling can be extended to the more general throughput problem in the real-time model. For the unweighted and proportionally weighted throughput problem (where the weight or value $w_i$ of a job $J_i$ is its processing time $p_i$), there are constant competitive real-time scheduling algorithms using preemption with restarting. More generally, the result for proportionally weighted interval scheduling can be extended to C-Benevolent weight functions. We also introduce a new real-time model in which jobs are announced before the actual release time of a job. We show that with sufficient advance notice, we can obtain a constant competitive ratio for proportionally weighted throughput {\it without any preemption}. However, this advance notice result does not extend to arbitrary C-Benevolent and D-Benevolent weight functions. Finally, we show that unlike interval scheduling, unweighted throughput using preemption with revoking admits no constant competitive ratio when the number of distinct processing times is unrestricted. More precisely, for instances with at most $k$ distinct processing times, we give a lower bound of $1/(k+1)$ and a deterministic $1/(2k)$-competitive algorithm.

cs.DS↗

arXiv2025

Revoke vs. Restart in Unweighted Throughput Scheduling

We study the unweighted throughput scheduling problem on a single machine in the preemption-revoke model, where a running job may be aborted at any time, but all progress is permanently lost and the job cannot be restarted. Each job $J_i=(r_i,p_i,s_i)$ is defined by a release time $r_i$, a processing time $p_i$, and a slack $s_i$, and must start no later than $r_i+s_i$ to be feasible. We prove that no deterministic online algorithm can achieve a constant competitive ratio. The lower bound is established via an adversarial construction: starting from a three-job instance where $\textsf{ALG}$ completes at most one job while $\textsf{OPT}$ completes all three, we iteratively nest such constructions. By induction, for every $k\ge 3$, there exists an instance where $\textsf{ALG}$ completes at most one job, while $\textsf{OPT}$ completes at least $k$ jobs. Thus, the competitive ratio can be forced to $1/k$, and hence made arbitrarily close to zero. Our result stands in sharp contrast to the preemption-restart model, where Hoogeveen, Potts, and Woeginger (2000) gave a deterministic $1/2$-competitive algorithm.

cs.DS↗