UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD

Serkan Güldal

doi:10.54365/adyumbd.980660

EN TR

UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD

Abstract

Modularity is a well-known method as a machine-learning algorithm to extract information from graphs. The modularity, in essence, divides the considered network into smaller clusters. The extracted clusters highlight the shared properties between the nodes in the same cluster. In the present study, we analyze the 6×6 knight graph by modularity method to obtain 6 Knight Covering Problem (6-KCP) solutions. Our investigation is ranged for the resolutions from 0.1 to 2.0. The maximum modularity score is 0.318 found for resolution 1.2. The resolutions, namely 0.3 and 0.4, identified all solutions, by 8 knights. Moreover, some solutions are obtained by 8 knights for the resolutions 0.2 and by 9, 10, 11, 12, 13 knights for the resolutions 0.2, 0.3, and 0.4. Moreover, resolution 0.3 is the most efficient resolution to find 6-KCP solutions. Also, within our analysis, resolution 0.2 is the best resolution to find more solutions, 195 solutions of 6-KCP. Lastly, the modularity method extracts the solutions from 61, for resolution 0.5, to 195, for resolution 0.2, out of 2253 solutions.

Keywords

Knight graph , modularity , Knight Covering Problem , Machine learning

6'YA 6 TAHTA ÜZERİNDE AT KAPLAMA PROBLEMİNİ ÇÖZMEK İÇİN DENETİMSİZ MAKİNE ÖĞRENME ALGORİTMASI

Öz

Modülerlik, çizgelerden bilgi çıkarmak için, çok kullanılan bir makine öğrenimi algoritmasıdır. Modülerlik, özünde, ele alınan ağı daha küçük kümelere böler. Oluşturan kümeler, aynı kümedeki düğümler arasındaki paylaşılan özellikleri vurgular. Bu çalışmada 6×6 at çizgesini modülerlik yöntemiyle analiz ederek 6 At Kaplama Probleminin (6-AKP) çözümlerini elde ettik. Araştırmamız 0,1 ile 2,0 arasındaki çözünürlükler için değişmektedir. Çözünürlük 1,2 için bulunan maksimum modülerlik puanı 0,318'dir. 0,3 ve 0,4 olmak üzere çözünürlükler, tüm çözümleri 8 at ile tanımladı. Ayrıca, 0,2 çözünürlükler için 8 at ve 0,2, 0,3 ve 0,4 çözünürlükler için 9, 10, 11, 12, 13 at ile bazı çözümler elde edilmektedir. Ayrıca, çözünürlük 0,3, 6-AKP çözümlerini bulmak için en verimli çözünürlüktür. Ayrıca, analizlerimiz gösterdi ki 0,2 çözünürlüğü, 6-AKP'nin 195 çözümünü daha fazla çözüm bulmak için en iyi çözünürlüktür. Son olarak, modülerlik yöntemi, 2253 çözüm arasından 0,5 çözünürlük için 61'den, 0,2 çözünürlük için 195'e kadar olan çözümleri çıkarıyor.

Anahtar Kelimeler

At çizgesi , modülerlik , At Kaplama Problemi , Makine öğrenmesi

Kaynakça

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Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Araştırma Makalesi

Yazarlar

Serkan Güldal ^*
0000-0002-4247-0786
Türkiye

Yayımlanma Tarihi

31 Aralık 2021

Gönderilme Tarihi

9 Ağustos 2021

Kabul Tarihi

25 Ekim 2021

Yayımlandığı Sayı

Yıl 1970 Cilt: 8 Sayı: 15

DOI

https://doi.org/10.54365/adyumbd.980660

IZ

https://izlik.org/JA34JM89UM

APA

Güldal, S. (2021). UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, 8(15), 414-426. https://doi.org/10.54365/adyumbd.980660

AMA

1.Güldal S. UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2021;8(15):414-426. doi:10.54365/adyumbd.980660

Chicago

Güldal, Serkan. 2021. “UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 8 (15): 414-26. https://doi.org/10.54365/adyumbd.980660.

EndNote

Güldal S (01 Aralık 2021) UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 8 15 414–426.

IEEE

[1]S. Güldal, “UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD”, Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, c. 8, sy 15, ss. 414–426, Ara. 2021, doi: 10.54365/adyumbd.980660.

ISNAD

Güldal, Serkan. “UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 8/15 (01 Aralık 2021): 414-426. https://doi.org/10.54365/adyumbd.980660.

JAMA

1.Güldal S. UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2021;8:414–426.

MLA

Güldal, Serkan. “UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, c. 8, sy 15, Aralık 2021, ss. 414-26, doi:10.54365/adyumbd.980660.

Vancouver

1.Serkan Güldal. UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 01 Aralık 2021;8(15):414-26. doi:10.54365/adyumbd.980660

UNSUPERVISED MACHINE LEARNING ALGORITHM TO SOLVE KNIGHT COVERING PROBLEM FOR 6 BY 6 BOARD

Abstract

Keywords

6'YA 6 TAHTA ÜZERİNDE AT KAPLAMA PROBLEMİNİ ÇÖZMEK İÇİN DENETİMSİZ MAKİNE ÖĞRENME ALGORİTMASI

Öz

Anahtar Kelimeler

Kaynakça

Ayrıntılar

Birincil Dil

Konular

Bölüm

Yazarlar

Yayımlanma Tarihi

Gönderilme Tarihi

Kabul Tarihi

Yayımlandığı Sayı

DOI

IZ

Kaynak Göster