Given a weighted directed graph G=(V;E;w), where w is non-negative weight function, G’ is a graph obtained from G by an application of path compression. Path compression reduces the graph G to a critical set of vertices and edges that affect the generation of shortest trees. The main contribution of this paper is finding shortest path between two selected vertices by applying a new algorithm that reduces number of nodes that needs to be traversed in the graph while preserving all graph properties.  The main method of the algorithm is restructuring the graph in a way that only critical/relevant nodes are considered while all other neutral vertices and weights are preserved as sub paths' properties.  Our algorithm can compress the graph paths into considerable improved percentage especially when the graph is sparse and hence improves performance significantly.

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Since the colloquial Arabic is now widespread it is required to describe the collection and classification of a multi-dialectal corpus of Arabic. Nowadays, colloquial multi-dialectal comes in almost country based forms such as Egyptian, Iraqi, Levantine, Tunisian, etc. This paper discusses a new method for analyzing the conversation of the educational chat room using Corpus for Palestinian Arabic and Stanford Tagger. This method represents the key words using semantic net-like representation to obtain the main subjects of the conversation. The main subject of the chat is obtained using the proposed method which shows a high accuracy. Using Arabic Corpus, Stanford Tagger and percentage of words will add more accuracy. The study also examines the effect of pivot distribution based on occurrences and <em>betweeness</em> values of the pivots over the text. This study examines some of the characteristics of the texts written in colloquial Arabic dialect and analyzes the free expressive Arabic statements. The results of the paper show that the core can be determined by combining both the occurrences and the distribution of the word over the conversation.