【摘要】：自然界中到處都存在著對稱性，對于具有對稱性的信息，在存儲時(shí)可根據(jù)它的特征進(jìn)行壓縮存儲。比如，如果平面圖形在二維坐標(biāo)系中是對稱的，則可以只存儲一半（不考慮對角線）的信息就可以表示出這個(gè)圖形，即可以存儲為一個(gè)上（或下）三角矩陣。類似的如果三維坐標(biāo)系是對稱的，就可以只存儲1/6（不考慮對角線）的信息，至于怎么存儲卻并不像二維對稱那樣簡單。在現(xiàn)實(shí)世界中，我們能夠觀察到的也就是三維，加上時(shí)間也才四維，但是在很多領(lǐng)域，經(jīng)常需要處理三維及三維以上的信息，，有時(shí)候這些多維信息，在維與維之間存在著對稱性。如果能夠像上（下）三角矩陣剝離二維對稱一樣去剝離多維信息中的對稱性，將可以極大地減少信息量，進(jìn)而降低存儲空間和處理時(shí)間。 本文針對上述問題，如果“多維空間”各維間具有對稱性，則其冗余程度是非常大的，較為系統(tǒng)的介紹了消除其冗余性的方法，即稱為“多維對稱空間壓縮存儲”的方法，并且設(shè)計(jì)了“遍歷多維對稱空間正對角面”的幾種高效的方法。首先，比較詳細(xì)的分析了“多維空間”的對稱性，通過坐標(biāo)映射的方式設(shè)計(jì)了多維對稱空間的壓縮存儲方法；然后分別設(shè)計(jì)了針對規(guī)整對稱空間正對角面，規(guī)整對稱空間，非對稱空間，非規(guī)整對稱空間的壓縮存儲方法；最后，還設(shè)計(jì)了“規(guī)整對稱空間正對角面遍歷”的方法。 此外，本文還將所設(shè)計(jì)的“多維對稱空間的壓縮存儲方法”應(yīng)用在小規(guī)模的多目標(biāo)0-1背包問題中，并經(jīng)過實(shí)驗(yàn)驗(yàn)證了它的正確性與有效性。實(shí)驗(yàn)結(jié)果表明，所設(shè)計(jì)的壓縮存儲方法是很有效的。所設(shè)計(jì)的“多維對稱空間的壓縮存儲方法”是一個(gè)非常有用的算法工具，可以極大的減少某些特定問題的內(nèi)存需要，進(jìn)而大大減少時(shí)間耗費(fèi)。
[Abstract]:Symmetry exists everywhere in nature. Information with symmetry can be compressed and stored according to its characteristics. For example, if a plane graph is symmetric in a two-dimensional coordinate system, it can be represented by only half of the information (not taking into account diagonals), that is, it can be stored as an upper (or lower) triangular matrix. Similarly, if the 3D coordinate system is symmetric, it can store only 1 / 6 of the information (without considering the diagonal), but how to store it is not as simple as the two-dimensional symmetry. In the real world, what we can observe is three dimensions, plus four dimensions of time, but in many areas, we often have to deal with three dimensional and more information, sometimes this multidimensional information. There is symmetry between dimension and dimension. If the symmetry in multidimensional information can be stripped off like the upper (lower) triangular matrix, the amount of information can be greatly reduced, and the storage space and processing time will be reduced. In order to solve the above problems, if there is symmetry among the dimensions of "multidimensional space", the degree of redundancy is very large. This paper systematically introduces the method of eliminating the redundancy, that is, the method of "multidimensional symmetric space compression storage". Several efficient methods of ergodic positive diagonal plane in multidimensional symmetric space are designed. Firstly, the symmetry of multidimensional space is analyzed in detail, and the compression storage method of multidimensional symmetric space is designed by coordinate mapping. Then, the compression storage methods for regular symmetric space, regular symmetric space and irregular symmetric space are designed, respectively, and the method of "regular symmetric space traversing positive diagonal plane" is also designed. In addition, the "compressed storage method of multidimensional symmetric space" is applied to the small scale multi-objective 0-1 knapsack problem, and its correctness and validity are verified by experiments. Experimental results show that the designed compression storage method is very effective. The "compressed storage method of multidimensional symmetric space" is a very useful algorithm tool, which can greatly reduce the memory needs of some specific problems, and thus greatly reduce the time consumption.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TP333

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