User talk:Mmohamadk

Introduction
The primary algorithm for finding shortest paths is Dijkstra's algorithm, which, efficiently finds the shortest paths from a given vertex x to all n-1 other vertices.Finding the shortest path in a network is a well studied problem that can be solved by efficient algorithms. A related problem is the K shortest path problem which the goal is not to identify the shortest path, but also the 2nd, 3rd, 4th... and the Kth shortest path from node s to t in a network.

De Queirosós Vieta Martins has written many references related to K shortest path problems, unfortunately it is very dificult to analize and understand the articles that have been written by Martins.

Labeling Algorithms
These algorithms behave much alike classical labeling algorithms for shortest paths problems. Consider the Kth shortest path from s to t. then anypart of this path is included in the jth shortest path from s to t with j<k. However, this principle is not satisfied in the case were only loopless paths are to be ranked.

Label correcting
A label correcting algorithm mainntains a list of labels at each node. K stands for the length of the list. One node is selected in each iteration and the associated label list is used to update other label lists. The label repeats until there are no more updates. A more efficient procedure of label correcting is to seperate labels and nodes. One single label is treated in each iteration rather than treating the whole label list at a node at once.

Label setting
The label setting algorithm is very similar to label correcting. The difference is that in each iteration, the label with the lowest cost in the network in chosen. Such a label is treated as a permanent label as in the Dijkstra's algorithm. This implies that the K shortest paths are ranked in order. Making a label at node t permanent identifies the next shortest path.

We call node i the deviation node of path K + 1. a deviation starts by searching for the shortest path tree from all other nodes to t. It then comes up with the shortest path, followed by considering all nodes along this paths as the deviation node. The paths' results are saved in a candidate list. The shortest path in this list is the second shortest one. In the next step, the algorithmb only needs to treat all nodes in the deviation part of the second shortest path as the deviation node and add some new possible paths to the list. The step are then repeated. Results have shown that deviation algorithms are very efficient.

Introduction
“It emerged in the 7th century CE and spread quickly throughout the Arabian peninsula and in several directions beyond. Within 100 years, the Arab empire extended from Spain and Morocco] in the west to beyond [[Persia in the east. Islam was the faith of its rulers. The map above shows the extent of Islam in about the year 750 CE.” (www.users. telerama.com) Islamic architecture can be traced back to the beginning in the 7th century CE, and continues on today. Islamic architecture includes the mosques, madrasas, caravansarais, palaces, and mausolea of this large region. There has been a faith that demonstrates both cultural unity and spiritual ideal at the heart of most civilizations that have lived through time. Until now, society has put forth a huge effort into searching for a higher spiritual level in the field of design. The Religion of Islam] is taught by Prophet [[Muhammad and is based on the holy Koran.

Islamic Concept
Islamic structures reflect older styles and concepts for several reasons. Many Islamic structures were built after older structures. Many concepts were taken from more ancient designs such as the column. The mosque is the most immediately recognizable and purely Islamic building. The Arab mosque is referred to as a hypostyle mosque. It usually includes a large courtyard and a low covered refuge. The roof could be flat or pitched, which is supported by many columns. One of the most distinctive features of the Iran]ian style is the extensive use of color and intricate geometric or organic designs. Walls and domes may be covered with such designs. The Iranian designes have been used in many mosques built in the east. “The Turkish or Ottoman mosque typically features a large dome and supporting piers. It is not a hypostyle mosque. Ceilings may be quite high and many smaller domes and half domes may be added. The exterior is somber and massive, and the exterior use of color is often quite limited.” (www.users.telerama.com) Islamic architecture is mostly know for its ornamentation in the deign. These design could be used on walls, and ceilings, domes (both inside and outside. Such art is also used as ceramics and rugs. Islamic ornamentation rarely uses human form; instead it surrounds three basic groups of design: •	Geometric forms •	Vegetal/organic forms •	Stylized Arabic script

According to Oleg Grabar, a Professor Emeritus at the Institute for Advanced Study in the School of Historical Studies, there are six basic principles describing Islamic ornamentation. They are as follow: •	"First, each object or wall is totally covered; no part is left without ornament. This is the celebrated horror vacui by which Islamic decoration has so often been defined." •	"Second, the ornament can best be defined as a relationship between forms rather than as a sum of forms. This relationship can most often be expressed in geometric terms...." •	"The impact of geometry is the third principle...." •	"...[T]he fourth principle of early Islamic ornament is the possibility of infinite growth, of which Mshatta's façade is the earliest illustration. On the one hand, the design can be extended at will in any direction...; it is the will of the decorator which defines the limits of the design. On the other hand, this type of design endows its observer with considerable freedom. He can choose the point of view from which he wishes to enjoy or appreciate a design like Mshatta's." •	"The fifth principle is that a theme from any origin could be and was incorporated in ornament. Although vegetal and geometric themes predominate, animal, human, and epigraphical ones exist as well." •	"The sixth and last principle, which sums up almost all the points made so far, is that of arbitrariness. The most consistent characteristic of most early Islamic ornament is that neither its size nor its internal forms are dictated by anything but itself." In other words, the ornament is not determined by the function of the building.