AI 中文总结
研究简单时态问题的最大可满足性（MAXSTP），分析其在变量数量\(n\)、最大系数幅度\(k\)、树宽\(tw\)和顶点覆盖大小\(vc\)等参数下的复杂性，给出相关算法，表明MAXSTP比定性CSP计算更难，部分问题以某些参数是固定参数可处理的。
AI 中文摘要
简单时态问题（STP）是定量时态约束的核心框架。由于STP数据可能不一致，我们研究MAXSTP：计算约束的最大基数一致子集。此扩展是NP难的，我们在捕获实际相关实例特征的度量下分析其参数化复杂性，包括变量数量\(n\)、最大系数幅度\(k\)以及约束图的结构参数如树宽\(tw\)和顶点覆盖大小\(vc\)。我们表明MAXSTP以\(n\)为参数是W[1]难的，意味着\(n\)和依赖于\(n\)的参数（包括\(tw\)和\(vc\)）不足以实现固定参数易处理性。对于组合参数，我们给出一个\(O^*(k^n)\)时间算法，对于固定的\(k\)产生单指数可解性。虽然\(k + tw\)仍然是W[1]难的，但MAXSTP通过一个\(O^*((n\cdot k)^{tw})\)算法属于XP。我们的结果表明MAXSTP通常比优化定性CSP计算上更难。我们验证许多此类问题（包括RCC - 8和Allen代数）以\(n\)或\(tw\)为参数时是固定参数可处理的。然而，我们也证明了MAXSTP的固定参数可处理算法确实是可能的，但使用其他参数如\(k + vc\)。
英文摘要
The Simple Temporal Problem (STP) is a core framework for quantitative temporal constraints. As STP data can be inconsistent, we study MAXSTP: compute a maximum-cardinality consistent subset of constraints. This extension is NP-hard, and we analyze its parameterized complexity under measures that capture practically relevant instance features: the number of variables $n$ (instance scale), the maximum coefficient magnitude $k$ (numeric range), and structural parameters of the constraint graph such as treewidth $tw$ (decomposability) and vertex cover size $vc$ (density). We show that MAXSTP is W[1]-hard parameterized by $n$, implying that $n$ and parameters that depend on $n$ (including $tw$ and $vc$) are insufficient for fixed-parameter tractability. For combined parameters, we give an $O^*(k^n)$-time algorithm, yielding single-exponential solvability for fixed $k$. While $k+tw$ remains W[1]-hard, MAXSTP is in XP via an $O^*((n\cdot k)^{tw})$ algorithm. Our results suggest that MAXSTP is often computationally harder than optimizing qualitative CSPs. We verify that many such problems (including RCC-8 and Allen's algebra) are FPT when parameterized by $n$ or $tw$. However, we also demonstrate that FPT algorithms for MAXSTP are indeed possible but with other parameters such as $k + vc$.
