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(4904031, 18.0377) (4905031, 18.0755) (4906031, 18.1143) (4907031, 18.1536) (4908031, 18.1928) (4909031, 18.2322) (4910031, 18.2696) (4911031, 18.3106) (4912031, 18.3513) (4913031, 18.3899) (4914031, 18.4302) (4915031, 18.4704) (4916031, 18.5113) (4917031, 18.553) (4918031, 18.5943) (4919031, 18.6374) (4920031, 18.6815) (4921031, 18.7225) (4922031, 18.7665) (4923031, 18.8096) (4924031, 18.8518) (4925031, 18.8949) (4926031, 18.9374) (4927031, 18.9776) (4928031, 19.0209) (4929031, 19.0651) (4930031, 19.1074) (4931031, 19.1514) (4932031, 19.1956) (4933031, 19.2401) (4934031, 19.2823) (4935031, 19.3273) (4936031, 19.375) (4937031, 19.4184) (4938031, 19.4634) (4939031, 19.5086) (4940031, 19.5564) (4941031, 19.6052) (4942031, 19.6517) (4943031, 19.698) (4944031, 19.7442) (4945031, 19.7905) (4946031, 19.8358) (4947031, 19.8853) (4948031, 19.9363) (4949031, 19.984) (4950031, 20.0341) (4951031, 20.084) (4952031, 20.1343) (4953031, 20.1863) (4954031, 20.2346) (4955031, 20.2858) (4956031, 20.3347) (4957031, 20.3866) (4958031, 20.4378) (4959031, 20.4888) (4960031, 20.5398) (4961031, 20.5928) (4962031, 20.6467) (4963031, 20.7002) (4964031, 20.7537) (4965031, 20.8064) (4966031, 20.8606) (4967031, 20.9115) (4968031, 20.9642) (4969031, 21.0237) (4970031, 21.081) (4971031, 21.1322) (4972031, 21.1858) (4973031, 21.2413) (4974031, 21.297) (4975031, 21.3497) (4976031, 21.4103) (4977031, 21.4654) (4978031, 21.5221) (4979031, 21.5806) (4980031, 21.6436) (4981031, 21.7026) (4982031, 21.7609) (4983031, 21.8187) (4984031, 21.8811) (4985031, 21.9419) (4986031, 22.0011) (4987031, 22.0606) (4988031, 22.1222) (4989031, 22.1792) (4990031, 22.2371) (4991031, 22.2984) (4992031, 22.3593) (4993031, 22.4185) (4994031, 22.4837) (4995031, 22.547) (4996031, 22.605) (4997031, 22.6669) (4998031, 22.7377) (4999031, 22.8035) (5000031, 22.8676) (5001031, 22.9344) (5002031, 23.002) (5003031, 23.0722) (5004031, 23.1389) (5005031, 23.2051) (5006031, 23.2706) (5007031, 23.3366) (5008031, 23.4057) (5009031, 23.475) (5010031, 23.5432) (5011031, 23.6119) (5012031, 23.6793) (5013031, 23.7477) (5014031, 23.8181) (5015031, 23.8897) (5016031, 23.9623) (5017031, 24.0371) (5018031, 24.1112) (5019031, 24.1854) (5020031, 24.2579) (5021031, 24.3328) (5022031, 24.4057) (5023031, 24.4794) (5024031, 24.5516) (5025031, 24.627) (5026031, 24.7) (5027031, 24.7759) (5028031, 24.8571) (5029031, 24.9333) (5030031, 25.0097) (5031031, 25.0909) (5032031, 25.1681) (5033031, 25.2457) (5034031, 25.3304) (5035031, 25.4132) (5036031, 25.4946) (5037031, 25.576) (5038031, 25.658) (5039031, 25.7402) (5040031, 25.8194) (5041031, 25.8983) (5042031, 25.9817) (5043031, 26.0676) (5044031, 26.1486) (5045031, 26.226) (5046031, 26.3095) (5047031, 26.4014) (5048031, 26.4851) (5049031, 26.5711) (5050031, 26.6563) (5051031, 26.7487) (5052031, 26.8368) (5053031, 26.9275) (5054031, 27.0161) (5055031, 27.0994) (5056031, 27.1864) (5057031, 27.2821) (5058031, 27.3681) (5059031, 27.4564) (5060031, 27.5539) (5061031, 27.645) (5062031, 27.7383) (5063031, 27.8328) (5064031, 27.9237) (5065031, 28.0164) (5066031, 28.1091) (5067031, 28.2076) (5068031, 28.3113) (5069031, 28.4134) (5070031, 28.5098) (5071031, 28.611) (5072031, 28.7128) (5073031, 28.821) (5074031, 28.9256) (5075031, 29.0283) (5076031, 29.13) (5077031, 29.2352) (5078031, 29.3367) (5079031, 29.4453) (5080031, 29.5521) (5081031, 29.659) (5082031, 29.7694) (5083031, 29.8865) (5084031, 30.001) (5085031, 30.1168) (5086031, 30.231) (5087031, 30.3474) (5088031, 30.4684) (5089031, 30.5872) (5090031, 30.7122) (5091031, 30.833) (5092031, 30.9485) (5093031, 31.0738) (5094031, 31.2017) (5095031, 31.3309) (5096031, 31.4597) (5097031, 31.5821) (5098031, 31.7111) (5099031, 31.8496) (5100031, 31.9888) (5101031, 32.1195) (5102031, 32.2541) (5103031, 32.3967) (5104031, 32.5441) (5105031, 32.6948) (5106031, 32.8359) (5107031, 32.9904) (5108031, 33.1399) (5109031, 33.2944) (5110031, 33.4554) (5111031, 33.6103) (5112031, 33.7684) (5113031, 33.9245) (5114031, 34.0873) (5115031, 34.2521) (5116031, 34.4206) (5117031, 34.5921) (5118031, 34.7722) (5119031, 34.9444) (5120031, 35.1188) (5121031, 35.2989) (5122031, 35.4781) (5123031, 35.6647) (5124031, 35.8596) (5125031, 36.0443) (5126031, 36.2382) (5127031, 36.4393) (5128031, 36.634) (5129031, 36.8311) (5130031, 37.0356) (5131031, 37.2406) (5132031, 37.4506) (5133031, 37.6678) (5134031, 37.8966) (5135031, 38.1221) (5136031, 38.3406) (5137031, 38.5848) (5138031, 38.8129) (5139031, 39.0487) (5140031, 39.3028) (5141031, 39.533) (5142031, 39.7754) (5143031, 40.0299) (5144031, 40.2928) (5145031, 40.5526) (5146031, 40.8226) (5147031, 41.0965) (5148031, 41.3671) (5149031, 41.648) (5150031, 41.945) (5151031, 42.242) (5152031, 42.5438) (5153031, 42.857) (5154031, 43.1842) (5155031, 43.502) (5156031, 43.8613) (5157031, 44.199) (5158031, 44.5533) (5159031, 44.9108) (5160031, 45.2559) (5161031, 45.6358) (5162031, 46.0109) (5163031, 46.4002) (5164031, 46.8151) (5165031, 47.2456) (5166031, 47.6581) (5167031, 48.0759) (5168031, 48.5231) (5169031, 48.9672) (5170031, 49.4339) (5171031, 49.9325) (5172031, 50.4214) (5173031, 50.9268) (5174031, 51.4333) (5175031, 51.9755) (5176031, 52.5225) (5177031, 53.073) (5178031, 53.6418) (5179031, 54.2313) (5180031, 54.8707) (5181031, 55.5656) (5182031, 56.2655) (5183031, 57.0185) (5184031, 57.7598) (5185031, 58.5164) (5186031, 59.2979) (5187031, 60.1783) (5188031, 61.0937) (5189031, 62.0647) (5190031, 63.0865) (5191031, 64.0722) (5192031, 65.2106) (5193031, 66.4051) (5194031, 67.56) (5195031, 68.8382) (5196031, 70.1711) (5197031, 71.5917) (5198031, 73.0805) (5199031, 74.682) (5200031, 76.4303) (5201031, 78.3868) (5202031, 80.3747) (5203031, 82.5966) (5204031, 84.9021) (5205031, 87.6316) (5206031, 90.6621) (5207031, 94.0534) (5208031, 97.8031) (5209031, 102.082) (5210031, 107.102) (5211031, 112.801) (5212031, 120.597) (5213031, 130.366) (5214031, 144.098) (5215031, 166.458) (5216031, 217.168) (5217031, 1494.03);

uncompressed LRAT (Mb), compressed DRAT (Mb);

Cactus plot of solving and verification times in seconds (left) and cactus plot of the size of the compressed DRAT proof and uncompressed LRAT proof in Mb (right).

For each cube, we produced a compressed DRAT proof (the default output of CaDiCaL). Due to the lack of hints in DRAT proofs,
they are somewhat complex to validate using a formally-verified checker. Instead, we use the tool drat-trim to trim the proofs
and add hints. The result are uncompressed LRAT files, which we validate using the formally-verified checker cake_lpr.
The verification time was 4336.93 CPU hours, so slightly less than the total runtime.

The sizes of each of the implication proofs show a similar distribution, as depicted in <Ref> (right).
Most proofs are less than 10 MB in size.
The compressed DRAT proofs are generally smaller
compared to the LRAT proofs, but that is mostly due to compression, which reduces the size by around 70%.

The Chessboard Conjecture and its Counterexample.

Given that color $1$ can be used to fill in $\nicefrac{1}{2}$ of $\mathbb{Z}^2$ in a packing coloring, and the packing colorings found in the past, with $15, 16$ or $17$ colors used color $1$ with density $\nicefrac{1}{2}$ in a chessboard pattern [18], it is tempting to assume that this must always be the case. This way, we conjectured that any instance $D_{r, k, c}$ is satisfiable if and only if it is with the chessboard pattern. The consequence of the conjecture is significant, as if it were true we could fix half of the vertices to color $1$, thus massively reducing the size of the instance and its runtime. Unfortunately, this conjecture happens to be false, with the smallest counterexample being $D_{14, 14, 6}$ as illustrated in <Ref>, which deviates from the chessboard pattern in only $2$ vertices. We have proved as well that no solution for $D_{14, 14, 6}$ deviating in only $1$ vertex from the chessboard pattern exists.

A valid coloring of $D_{14,14,6}$. No valid coloring exists for this grid with a full chessboard pattern of 1's.

Proving the Lower Bound.

In order to prove <Ref>, we require the following $3$ lemmas, from where the conclusion easily follows.

If $D_{15, 14, 6}$ is unsatisfiable, then $\chi_\rho(\mathbb{Z}^2) \geq 15$.

If $D_{15, 14, 6}$ is satisfiable, then $P^\star_{15, 14, 6}$ is also satisfiable.

$P^\star_{15, 14, 6}$ is unsatisfiable.

We have obtained computational proofs of <Ref> and <Ref> as described above, and thus it only remains to prove <Ref>, which we include in the appendix. We can thus proceed to our main proof.

Since Martin et al. proved that $\chi_\rho(\mathbb{Z}^2) \leq 15$ [18], it remains to show $\chi_\rho(\mathbb{Z}^2) \geq 15$, which by <Ref> reduces to proving <Ref> and <Ref>. We have proved these lemmas computationally, obtaining a single DRAT proof as described in <Ref>.
The total solving time was $4851.31$ CPU hours, while the total checking time of the proofs was $4336.93$ CPU hours. The total size of the compressed DRAT proof is $34$ terabytes, while the uncompressed LRAT proof weighs $122$ terabytes.

§ CONCLUDING REMARKS AND FUTURE WORK

We have proved $\chi_\rho(\mathbb{Z}^2) = 15$ by using several SAT-solving techniques, in what constitutes a new
success story for automated reasoning tools applied to combinatorial problems. Moreover, we believe that several of our contributions in this work might be applicable to other settings and problems. Indeed, we have obtained a better encoding by reverse engineering BVA, and designed a split algorithm that works well coupled with the new encoding; this experience suggests the split-encoding compatibility as a new key variable to pay attention to when solving combinatorial problems under the paradigm. As for future work, it is natural to study whether our techniques can be used to improve other known bounds in the packing-coloring area (see e.g., [3]), as well as to other families of coloring problems, such as distance colorings [14].

[1]
Appel, K., Haken, W.: Every planar map is four colorable. Part I:
Discharging. Illinois Journal of Mathematics  21(3),  429 – 490

[2]
Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat,
Paracooba, Plingeling and Treengeling entering the SAT Competition
2020. In: Balyo, T., Froleyks, N., Heule, M., Iser, M., Järvisalo, M.,
Suda, M. (eds.) Proc. of SAT Competition 2020 – Solver and Benchmark
Descriptions. Department of Computer Science Report Series B, vol. B-2020-1,
pp. 51–53. University of Helsinki (2020)

[3]
Brešar, B., Ferme, J., Klavžar, S., Rall, D.F.: A survey on packing
colorings. Discussiones Mathematicae Graph Theory  40(4),  923

[4]
Brown, S.T., Buitrago, P., Hanna, E., Sanielevici, S., Scibek, R., Nystrom,
N.A.: Bridges-2: A Platform for Rapidly-Evolving and Data Intensive Research,
pp. 1–4. Association for Computing Machinery, New York, NY, USA (2021)

[5]
Buss, S., Thapen, N.: DRAT proofs, propagation redundancy, and extended
resolution. In: Janota, M., Lynce, I. (eds.) Theory and Applications of
Satisfiability Testing – SAT 2019. pp. 71–89. Springer International
Publishing, Cham (2019)

[6]
Crawford, J., Ginsberg, M., Luks, E., Roy, A.: Symmetry-breaking predicates for
search problems. In: Proc. KR'96, 5th Int. Conf. on Knowledge Representation
and Reasoning, pp. 148–159. Morgan Kaufmann (1996)

[7]
Ekstein, J., Fiala, J., Holub, P., Lidický, B.: The packing chromatic
number of the square lattice is at least 12. CoRR  abs/1003.2291
(2010), <http://arxiv.org/abs/1003.2291>

[8]
Fiala, J., Klavžar, S., Lidický, B.: The packing chromatic number of
infinite product graphs. Eur. J. Comb.  30(5),  1101–1113 (jul

[9]
Finbow, A.S., Rall, D.F.: On the packing chromatic number of some lattices.
Discrete Applied Mathematics  158(12),  1224–1228 (2010), traces
from LAGOS'07 IV Latin American Algorithms, Graphs, and Optimization
Symposium Puerto Varas - 2007

[10]
Goddard, W., Hedetniemi, S., Hedetniemi, S., Harris, J., Rall, D.: Broadcast
chromatic numbers of graphs. Ars Comb.  86 (01 2008)

[11]
Heule, M.J.H.: The DRAT format and drat-trim checker. CoRR
abs/1610.06229 (2016), <http://arxiv.org/abs/1610.06229>

[12]
Heule, M.J.H., Biere, A.: What a difference a variable makes. In: Beyer, D.,
Huisman, M. (eds.) Tools and Algorithms for the Construction and Analysis of
Systems. pp. 75–92. Springer International Publishing, Cham (2018)

[13]
Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding
CDCL SAT solvers by lookaheads. In: Eder, K., Lourenço, J.,
Shehory, O. (eds.) Hardware and Software: Verification and Testing. pp.
50–65. Springer Berlin Heidelberg, Berlin, Heidelberg (2012)

[14]
Kramer, F., Kramer, H.: A survey on the distance-colouring of graphs. Discrete
Mathematics  308(2),  422–426 (2008)

[15]
Kullmann, O.: On a generalization of extended resolution. Discrete Applied
Mathematics  96-97,  149–176 (1999)

[16]
Manthey, N., Heule, M.J.H., Biere, A.: Automated reencoding of boolean
formulas. In: Proceedings of Haifa Verification Conference 2012 (2012)

[17]
Martin, B., Raimondi, F., Chen, T., Martin, J.: The packing chromatic number of
the infinite square lattice is less than or equal to 16 (2015),

[18]
Martin, B., Raimondi, F., Chen, T., Martin, J.: The packing chromatic number of
the infinite square lattice is between 13 and 15. Discrete Applied
Mathematics  225,  136–142 (2017)

[19]
Neiman, D., Mackey, J., Heule, M.J.H.: Tighter bounds on directed Ramsey
number R(7). Graphs and Combinatorics  38(5),  156 (2022)

[20]
Schwenk, A.: private communication with Wayne Goddard. (2002)

[21]
Soifer, A.: The Hadwiger–Nelson Problem, pp. 439–457. Springer International
Publishing, Cham (2016)

[22]
Soukal, R., Holub, P.: A note on packing chromatic number of the square
lattice. The Electronic Journal of Combinatorics  17(1),  #N17 (Mar

[23]
Subercaseaux, B., Heule, M.J.H.: The Packing Chromatic Number of the Infinite
Square Grid Is at Least 14. In: Meel, K.S., Strichman, O. (eds.) 25th
International Conference on Theory and Applications of Satisfiability Testing
(SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs),
vol. 236, pp. 21:1–21:16. Schloss Dagstuhl – Leibniz-Zentrum für
Informatik, Dagstuhl, Germany (2022)

§ APPENDIX

§ DETAILS OF THE PLUS ENCODING

Let us use notation $\Delta(v, S) := \max_{u \in S} d(u, v),$ and similarly $\Delta(S_1, S_2) := \max_{u \in S_1} \Delta(u, S_2)$.
Then, the $\textsf{plus}$ encoding $P_{r, k, c}$, with a set $R$ of variables $r_{S_i, c_i}$, consists of the following kinds of clauses:

* (at-least-one-color clauses, aloc)

\[
\bigvee_{t=1}^k x_{v, t}, \quad \forall v \in V,\]

* (region definition clauses)

\[
\overline{r_{S_i, c_i}} \lor \bigvee_{v \in S_i} x_{v, c_i}, \quad \forall r_{S_i, c_i} \in R,
\]

* (region membership clauses)

\[
r_{S_i, c_i} \lor \overline{x_{v, c_i}}, \quad \forall r_{S_i, c_i} \in R, \forall v \in S_i,
\]

* (region-vertex distance clauses)

\[
\overline{r_{S_i, c_i}}\lor \overline{x_{v, c_i}}, \quad \forall r_{S_i, c_i} \in R, \forall v \in V \text{ s.t. } \Delta(v, S_i) \leq c_i,
\]

* (region-region distance clauses)

\[
\overline{r_{S_i, c_i}}\lor \overline{r_{S_j, c_i}}, \quad \forall r_{S_i, c_i} \in R, \forall r_{S_j, c_i} \in R\text{ s.t. } \Delta(S_i, S_j) \leq c_i \text{ and } S_i \neq S_j,
\]

* (at-most-one distance clauses, amod)
\[
\overline{x_{u,t}} \lor \overline{x_{v,t}}, \quad \forall t \in [k], \forall u, v \in V \text{ s.t. } d(u, v) \leq t, \text { and not covered by cases 4 or 5},
\]

* (center clause)
\( \quad \quad
x_{(0, 0), c}.
\)

To be even more precise about the $6^{\text{th}}$ kind of clauses, two vertices $u$ and $v$ at distance $d$ require clauses to forbid that they both take any color $t \leq d$. The $4$-th and $5$-th kind of clauses cover some of those cases, while leaving some cases uncovered. Thus, all clauses of kind $4$ or $5$ must be added first, and then clauses of kind $6$ must complete the remaining cases.

§ ALGORITHM FOR CONSTRUCTING THE CUBES

CubeConstruction$(P, T, R, k, c)$; ptr algorithm.

$\textrm{topColors} \gets \{k, k-1, \ldots, k-T+1\}$

$i \in \emph{topColors}$
$\textrm{NV}_i \gets R \text{ new variables corresponding to the regions of color } i \text{ that are closest to the center.}$

$c \in \emph{topColors}$

$\textrm{topColors} \gets \textrm{topColors} \cup \{ k- T \}$
$\textrm{topColors} \gets \textrm{topColors} \setminus \{ c \}$

$ \textrm{cubes} \gets \emptyset$
$p \in \{P, P-1, \ldots, 0\}$
$\emph{colorSet} \subseteq \emph{topColors}, \, \emph{s.t. } |\emph{colorSet}| = p$

$\textrm{products} \gets \textrm{NV}_{c_1} \times \textrm{NV}_{c_2} \times \cdots \times \textrm{NV}_{c_p
}$, for $c_i \in \textrm{colorSet}$.
$\textrm{negatives} \gets \emptyset$

$p \neq P$
$\emph{color} \in \emph{topColors} \setminus \emph{colorSet}$
$\textrm{negatives} \gets \textrm{negatives} \cup \left(\bigcup_{S \in \textrm{NV}_{color}} \{ \overline{r_{S, \textrm{color}}}\}\right)$

$\emph{product} \in \emph{products}$
$\textrm{cubes} \gets \textrm{cubes} \cup \{\{ \textrm{product} \cup \textrm{negatives} \}\}$

It is worth noting that in line $1.3$ of Algorithm <ref>, the notion of closest to the center corresponds to a distance between a set $S$ of vertices and a given vertex $u$ (i.e., the center), which is defined simply as $d(u, S) = \min_{v \in S} d(u, v).$

§ CODE FOR GENERATING THE DIRECT ENCODING

[language=Python, caption=Implementation of the direct encoding in Python 3.10.,label=lst:direct-encoding]direct-mini.py

§ PROOF OF LEMMA 2

Let us prove something slightly more general, from where the lemma follows as a particular case: that if $D_{r, k, c}$ is unsatisfiable, for some value $k$ and $\chi_\rho(\mathbb{Z}^2) \geq k$, regardless of the values of $r$ and $c \leq k$, then $\chi_\rho(\mathbb{Z}^2) \geq k+1$.

Indeed, assume expecting a contradiction that $\chi_\rho(\mathbb{Z}^2) \geq k$ and  $D_{r, k, c}$ is unsatisfiable, but $\chi_\rho(\mathbb{Z}^2) \not\geq k+1$. As $\chi_\rho(\mathbb{Z}^2) \leq k$, there is a packing $k$-coloring $\varphi$ for $\mathbb{Z}^2$. Moreover, $\varphi$ must use color $k$ for at least one vertex, as we are assuming $\chi_\rho(\mathbb{Z}^2) \geq k$. There are now two cases. If $\varphi$ assigns color $c$ to some vertex $v$, then $D_{r, k, c}$ must be satisfiable, as restricting $\varphi$ to the $\ell_1$-ball of radius $r$  centered around $v$ gives us a satisfying assignment for $D_{r, k, c}$, which directly contradicts our assumption. If  $\varphi$ does not assign color $c$ to any vertex $v$, then let $\varphi'$ be equal to $\varphi$ except that $\varphi'$ assigns color $c$ to every vertex $v$ that $\varphi$ assigned color $k$. Note that $\varphi'$ is a valid packing coloring, as it only differs from $\varphi$ in that it has assigned color $c$ to vertices that had color $k$ before, and as $c \leq k$, this cannot create any conflicts, and $\varphi$ was assumed to not assign color $c$ to any vertex, so the newly colored $c$ vertices in $\varphi'$ cannot create conflicts at all. But as a result $\varphi'$ does not assign color $k$ to any vertex (note that it cannot be that $c = k$, as we have already established that $\varphi$ needs to assign color $k$ to at least one vertex given that $\chi_\rho(\mathbb{Z}^2) \geq k$), and thus $\varphi'$ is a packing $k-1$-coloring of $\mathbb{Z}^2$, which contradicts the assumption that $\chi_\rho(\mathbb{Z}^2) \geq k$. This concludes the proof.