通过分析欧拉所给出Knight’s Tour Problem的解法,结合哈密尔顿路和哈密尔顿圈的相关知识,得出其解法对应着二部图中的一条哈密尔顿圈.由此再充分利用8×8棋盘所对应的8×8表格的对称性及同格图的特性,对欧拉所给出的Knight’s...通过分析欧拉所给出Knight’s Tour Problem的解法,结合哈密尔顿路和哈密尔顿圈的相关知识,得出其解法对应着二部图中的一条哈密尔顿圈.由此再充分利用8×8棋盘所对应的8×8表格的对称性及同格图的特性,对欧拉所给出的Knight’s Tour Problem的解法作了进一步的探讨,得出了以欧拉的解法为基础的以任一棋格为骑士周游起点的另外一系列解法.最后,把Knight’sTour Problem推广到m×n棋盘上,考虑到移动规则的特殊性,利用图论的相关知识,得到3×4,8×16和16×16棋盘上的Knight’s Tour Problem的解法,同时给出8m×8n(m>2,n>2)棋盘上Knight’s Tour Problem的猜想.展开更多
The security of critical data is an important issue for distributed storage system design,especially for long-term storage.ESSA (An Efficient and Secure Splitting Algorithm for Distributed Storage Systems) is presente...The security of critical data is an important issue for distributed storage system design,especially for long-term storage.ESSA (An Efficient and Secure Splitting Algorithm for Distributed Storage Systems) is presented,which takes advantage of a two level information dispersal scheme to strengthen the security of data.In ESSA,the approach of knight’s tour problem,which is NP-Complete,is introduced to scramble data at the first level,and a split cube is used to split scrambled data at the second level.Thus,it is very difficult for the malicious user to get information because the task of reconstructing the original data needs more computation than they can tolerate.We prove that the security of ESSA is better than encryption algorithm and not inferior to erasure codes and secret sharing.Experimental results show that distributed storage systems exploiting ESSA has greater efficiency than that exploiting keyed encryption,erasure codes and secret sharing.展开更多
文摘通过分析欧拉所给出Knight’s Tour Problem的解法,结合哈密尔顿路和哈密尔顿圈的相关知识,得出其解法对应着二部图中的一条哈密尔顿圈.由此再充分利用8×8棋盘所对应的8×8表格的对称性及同格图的特性,对欧拉所给出的Knight’s Tour Problem的解法作了进一步的探讨,得出了以欧拉的解法为基础的以任一棋格为骑士周游起点的另外一系列解法.最后,把Knight’sTour Problem推广到m×n棋盘上,考虑到移动规则的特殊性,利用图论的相关知识,得到3×4,8×16和16×16棋盘上的Knight’s Tour Problem的解法,同时给出8m×8n(m>2,n>2)棋盘上Knight’s Tour Problem的猜想.
基金This study is supported by National Natural Science Foundation of China （No.60973146） National Natur al Science Foundation of Beijing （No.4092029） The Fundamental Research Funds for the Central Universities （No.2009RC0217）. We also thank the anonymous reviewers for their constructive comments.
文摘The security of critical data is an important issue for distributed storage system design,especially for long-term storage.ESSA (An Efficient and Secure Splitting Algorithm for Distributed Storage Systems) is presented,which takes advantage of a two level information dispersal scheme to strengthen the security of data.In ESSA,the approach of knight’s tour problem,which is NP-Complete,is introduced to scramble data at the first level,and a split cube is used to split scrambled data at the second level.Thus,it is very difficult for the malicious user to get information because the task of reconstructing the original data needs more computation than they can tolerate.We prove that the security of ESSA is better than encryption algorithm and not inferior to erasure codes and secret sharing.Experimental results show that distributed storage systems exploiting ESSA has greater efficiency than that exploiting keyed encryption,erasure codes and secret sharing.
