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Computer Science / Algorithms / Network Optimisation

An Improved Dijkstra’s Shortest Path Algorithm for Sparse Networks

This technical research paper investigates an improved version of Dijkstra’s shortest path algorithm for sparse weighted networks. Traditional implementations of Dijkstra’s algorithm can achieve a time complexity of O(m + n log n) when Fibonacci heaps are used, but the authors argue that heap construction increases implementation complexity. The proposed approach modifies the original algorithm so that heap construction is avoided while maintaining competitive performance on sparse graphs. An_improved_Dijkstra’s_shortest… The study focuses on the single-source shortest path problem in weighted directed graphs with non-negative edge lengths. It begins by reviewing a refined Dijkstra algorithm in which each vertex maintains a distance label representing an upper bound on the shortest distance from the source vertex. The main computational bottleneck is repeatedly identifying the unvisited vertex with the smallest distance label. A naïve implementation requires O(n²) time, while Fibonacci-heap implementations improve efficiency but introduce additional implementation complexity. An_improved_Dijkstra’s_shortest… An_improved_Dijkstra’s_shortest… The authors propose an improved Dijkstra algorithm that maintains distance labels in an ordered list. When a distance label changes, the corresponding entry is reinserted into the appropriate location rather than rebuilding or maintaining a heap. The algorithm exploits the characteristics of sparse networks, where each vertex is connected to only a relatively small number of edges. This is particularly relevant to road networks, where the maximum degree of each node is typically low. An_improved_Dijkstra’s_shortest… To support efficient reinsertion, the paper introduces a predefined step-size vector and a binary-search-style process for locating the correct insertion position. This approach reduces the number of comparisons required while avoiding the division operations commonly associated with standard binary search implementations. An_improved_Dijkstra’s_shortest… An_improved_Dijkstra’s_shortest… The theoretical analysis shows that the proposed method requires approximately O(m + Dmax log(n!)) comparisons and arithmetic operations, where m represents the number of edges and Dmax is the maximum number of edges incident on a vertex. The authors argue that this complexity makes the approach especially suitable for large-scale sparse networks where the maximum node degree remains relatively small. An_improved_Dijkstra’s_shortest… An_improved_Dijkstra’s_shortest… The algorithm is evaluated through numerical experiments implemented in MATLAB. Two families of randomly generated sparse networks are tested, with network sizes ranging from approximately 10,000 to 21,000 nodes. The first experiment uses a maximum node degree of four, while the second uses a maximum degree of six. Experimental ratios reported in the paper remain close to the theoretical complexity estimate as network size increases. An_improved_Dijkstra’s_shortest… The paper concludes that the improved Dijkstra approach is practical for large sparse networks, particularly road-traffic networks. By avoiding Fibonacci-heap construction and using an ordered-list reinsertion strategy, the algorithm aims to simplify implementation while maintaining competitive computational performance for shortest-path calculations. An_improved_Dijkstra’s_shortest… Important: because this is a published journal article rather than a university assignment brief, fields such as module name, assessment level and assignment word count are not stated in the source. For the portal, it is safer to use Not specified / Not applicable for those fields rather than inventing academic-assessment details.

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Computer Science / Algorithms / Computational Complexity

Modified Merge Sort for Large-Scale Data: Algorithm Analysis, Complexity and Evaluation

This Computational Algorithms and Paradigms assignment critically examines a modified merge sort algorithm designed for large-scale datasets. The work focuses on the computational problem of sorting very large collections of data efficiently while preserving the stability and predictable complexity associated with classical merge sort. The analysed approach replaces recursive processing with an iterative successive-merging strategy intended to reduce stack overhead and improve practical performance on large datasets. Dubba ramesh(up) The first section identifies the underlying computational problem and frames the main research questions. These include how standard merge sort can be modified to improve large-scale performance, whether recursion can be replaced with a non-recursive iterative process, whether the proposed double-merge technique reduces resource consumption, and how its computational performance compares with classical merge sort. Dubba ramesh(up) A technical section then reconstructs the algorithm in pseudocode. The modified process begins with subsequences of size one and repeatedly merges adjacent sorted subsequences, doubling the merge size after each iteration until the entire dataset is sorted. This bottom-up approach removes the recursive decomposition used in conventional merge sort. Dubba ramesh(up) The assignment also identifies the algorithm's principal inputs and outputs. Inputs include the dataset, number of elements, subsequence boundaries and temporary storage required during merging. The resulting output is a fully sorted and stable sequence. Dubba ramesh(up) Complexity analysis shows that the modified algorithm processes approximately n elements across log₂(n) merging levels, resulting in O(n log n) time complexity in both best and worst cases. Because an auxiliary array is used during merging, the reported space complexity is O(n). Dubba ramesh(up) The final critical evaluation highlights the main benefits of the modified approach, including removal of recursive-call overhead, greater stability when processing very large datasets, predictable performance and preservation of merge-sort stability. Its main limitation is the continued requirement for auxiliary memory during the merge operation. The work also notes that the performance advantages are most relevant for large-scale datasets and may be less significant for smaller inputs. Dubba ramesh(up) Overall, the assignment integrates algorithm interpretation, pseudocode extraction, input-output analysis, complexity analysis and critical evaluation within the context of large-scale sorting. Note: this upload appears to be the completed student response rather than the original assessment brief, so the referencing style and exact formal overall word limit are not stated. I would leave the reference-style field as Not specified unless you also upload the official 7COM1078 guideline.

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