arXiv subjects

Jorke M. de Vlas

Publications and source records attributed to Jorke M. de Vlas.

3 recordsLinked to original sources

arXiv2026

Maximum Satisfiability of Simple Temporal Problems

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 $k + vc$.

cs.CC↗

arXiv2025

Going Beyond Twin-width? CSPs with Unbounded Domain and Few Variables

We study a model of constraint satisfaction problems geared towards instances with few variables but with domain of unbounded size (udCSP). Our model is inspired by recent work on FPT algorithms for MinCSP where frequently both upper and lower bounds on the parameterized complexity of a problem correspond to $k$-variable udCSPs; e.g., the FPT algorithms for Boolean MinCSP (Kim et al., SODA 2023) and Directed Multicut with three cut requests (Hatzel et al., SODA 2023) both reduce to k-variable udCSPs, and the canonical W[1]-hardness construction in the area, Paired Min Cut by Marx and Razgon (IPL 2009), is effectively a k-variable udCSP. The udCSP framework represents constraints with unbounded domains via a collection $\mathcal{M}$ of unary maps into a finite-domain base language $Γ$. We develop an algebraic theory for studying the complexity of udCSP$(Γ,\mathcal{M})$ with a Galois connection based on partial multifunctions. We study three types of maps: unrestricted, one-hot, and monotone. For unrestricted maps, the problem is W[1]-hard for all but trivial cases, and for one-hot maps, the characterization coincides with Marx' FPT dichotomy for Boolean Weighted CSPs (Computational Complexity 2005). For the case of monotone maps Mo, we show that the complexity depends on restricted identifies we call ordered polymorphisms; we identify the "connector" polymorphism as the likely FPT boundary. We show that its absence implies that udCSP($Γ$,Mo) defines all permutations, and the problem is W[1]-hard; while its presence for a binary language implies bounded twin-width, and the problem is FPT (Twin-Width IV; Bonnet et al., JACM 2024). For non-binary languages, where twin-width does not apply, the polymorphism coincides with a notion of bounded projected grid-rank; however, we leave the FPT question for this case open.

cs.DS↗

arXiv2023

On the Parameterized Complexity of the Perfect Phylogeny Problem

This paper categorizes the parameterized complexity of the algorithmic problems Perfect Phylogeny and Triangulating Colored Graphs when parameterized by the number of genes and colors, respectively. We show that they are complete for the parameterized complexity class XALP using a reduction from Tree-chained Multicolor Independent Set and a proof of membership. We introduce the problem Triangulating Multicolored Graphs as a stepping stone and prove XALP-completeness for this problem as well. We also show that, assuming the Exponential Time Hypothesis, there exists no algorithm that solves any of these problems in time $f(k) n^{o(k)}$, where $n$ is the input size, $k$ the parameter, and $f$ any computable function.

cs.CC↗