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An efficient algorithm for finding a shortest paths for all vertices in graph

خوارزمية فعالة لإيجاد المسارات الأقصر لجميع العقد في البيان

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 Publication date 2015
and research's language is العربية
 Created by zeina alrostum




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The all-nodes shortest paths problem is undoubtedly one of the most basic problems in algorithmic graph theory. In this paper, we introduce simple and efficient algorithm for all nodes shortest paths problem for directed (undirected) graphs. In this problem, we find the shortest path from a given source node to all other nodes in the graph, in which the shortest path is a path with minimum cost, i.e., sum of the edge weights. We proved that the complexity of the proposed algorithm in this paper depends only on the edges graph, and we show that the time of implementation of this algorithm is linear time O(m) and This is considered the best times of the algorithms at all. And a Comparison between complexity of proposed algorithm and the famous shortest path algorithms have been made, and the obtained results have shown that the complexity of the proposed algorithm is best.


Artificial intelligence review:
Research summary
تتناول هذه الورقة البحثية مسألة إيجاد المسارات الأقصر لجميع العقد في بيان موجه أو غير موجه. يقدم الباحث د. محسن حسين خوارزمية جديدة وفعالة لهذه المسألة، حيث يتم إيجاد المسار الأقصر من عقدة منبع معينة إلى جميع العقد الأخرى في البيان. تعتمد الخوارزمية المقترحة على زمن خطي قدره O(m)، مما يجعلها من أفضل الخوارزميات من حيث زمن التنفيذ. تم إجراء مقارنة بين تعقيد الخوارزمية المقترحة وتعقيد الخوارزميات الشهيرة الأخرى، وتبين أن الخوارزمية المقترحة هي الأفضل. كما تم تقديم مثال توضيحي لعمل الخوارزمية وتحليل شامل لدرجة تعقيدها وزمن تنفيذها. الخوارزمية المقترحة تتميز بأنها بسيطة وسهلة التنفيذ ويمكن برمجتها حاسوبياً بسهولة، كما يمكن تطبيقها على بيانات كبيرة الحجم.
Critical review
دراسة نقدية: تعتبر هذه الورقة البحثية إضافة قيمة لمجال نظرية البيان وخوارزميات المسار الأقصر. ومع ذلك، هناك بعض النقاط التي يمكن تحسينها. أولاً، كان من الممكن تقديم المزيد من الأمثلة العملية لتوضيح كيفية تطبيق الخوارزمية على بيانات حقيقية. ثانياً، لم يتم التطرق بشكل كافٍ إلى كيفية تعامل الخوارزمية مع البيانات التي تحتوي على أوزان سالبة، وهو ما يمكن أن يكون تحدياً في بعض التطبيقات. أخيراً، كان من الممكن تقديم تحليل أكثر تفصيلاً لمقارنة الأداء بين الخوارزمية المقترحة والخوارزميات الأخرى في ظروف مختلفة.
Questions related to the research
  1. ما هي المسألة الرئيسية التي تتناولها الورقة البحثية؟

    المسألة الرئيسية هي إيجاد المسارات الأقصر لجميع العقد في بيان موجه أو غير موجه.

  2. ما هو زمن تنفيذ الخوارزمية المقترحة؟

    زمن تنفيذ الخوارزمية المقترحة هو زمن خطي قدره O(m).

  3. ما هي الميزة الرئيسية للخوارزمية المقترحة مقارنة بالخوارزميات الأخرى؟

    الميزة الرئيسية هي أن زمن تنفيذها خطي، مما يجعلها من أفضل الخوارزميات من حيث زمن التنفيذ.

  4. هل يمكن تطبيق الخوارزمية على بيانات كبيرة الحجم؟

    نعم، يمكن تطبيق الخوارزمية على بيانات كبيرة الحجم لأن زمن تنفيذها لا يعتمد على عدد العقد في البيان.


References used
Allulli. L, Lichodzijewski .P and Zeh. N, "A Faster Cache- Oblivious Shortest-Path Algorithm for Undirected Graphs with Bounded Edge Lengths", www.web.cs.dal.ca
BASWANA. S AND KAVITHA. T, "FASTER ALGORITHMS FOR ALL-PAIRS APPROXIMATE SHORTEST PATHS IN UNDIRECTED GRAPHs", Jornal of ACM,52(1), pp 1- 24. 2005. www.cse.iitk.ac.in
Bernstein. A, "Near Linear Time (1 + ϵ)-Approximation for Restricted Shortest Paths in Undirected Graphs", siam, 2011
Brandes. U, "A Faster Algorithm for Betweenness Centrality", Journal of Mathematical Sociology 25(2):163-177, (2001)
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