Arc Consistency Revisited

Generalized Arc Consistency Algorithms for Table Constraints: A Summary of Algorithmic Ideas

“…Recent work with the HTAC algorithm (Wang and Yap 2019) suggests that although most research has focused on GAC algorithms rather than AC algorithms over the past decades, the binary case may need to be revisited. Indeed, HTAC uses techniques used in recent GAC algorithms, but specialised to the binary case and the hidden variable encoding.…”

“…Most research (over the past decade and more) has been on the former as it was believed that binary encoding is not practical. The reason for this belief is shown with experiments in Wang and Yap (Wang and Yap 2019) showing that dual encoding takes too much space and HVE with the best AC algorithms (AC3 bit and HAC (Mamoulis and Stergiou 2001;Samaras and Stergiou 2005)) are considerably outperformed by CT on the original non-binary CSP. However the HTAC algorithms in (Wang and Yap 2019) were shown to be competitive with state-of-art CT and STRbit.…”

“…Figure 1 shows the algorithmic improvements over time, for selected GAC algorithms on a diverse set of instances. 1 Newer algorithms such as GAC-VA (Lecoutre and Szymanek 2006), STR2+ (Lecoutre 2008;, STR3 (Lecoutre, Likitvivatanavong, and Yap 2012;2015b), and Mddc (Cheng and Yap 2008;2010) are faster than the older GAC-4 (Mohr and Masini 1988), GAC-V, and GAC-A (Bessière and Régin 1997) but slower than the even newer algorithms such as STRbit (Wang et al 2016), CT (Demeulenaere et al 2016) and HTAC (Wang and Yap 2019), e.g. on the Crossword-ogd-vg-11-13 instance-GAC-A timeouts, CT takes 49.78s and HTAC is the fastest at 21.97s (this problem instance is also in Figure 1).…”

Encoding Multi-Valued Decision Diagram Constraints as Binary Constraint Trees

“…The BCT is a binary CSP with a special structure, which we exploit to devise more efficient propagators. We follow the ideas of special propagation order in the HTAC algorithm (Wang and Yap 2019). Given any TBE (X, C) of a constraint c * , the constraint graph of (X, C) is a tree.…”

“…For each binary constraint c ∈ C between 2 variables x, y, if x / ∈ H 1 or y / ∈ H 1 , i.e. there is one variable whose domain is not represented as (sparse) bit set, we can directly use the existing revise functions introduced in (Lecoutre and Vion 2008;Wang and Yap 2019), otherwise we apply a new revise function (Algorithm 2) given below for the case when both variables are sparse bit sets.…”