A Slightly Improved Sub-cubic Algorithm for the All Pairs Shortest Paths Problem with Real Edge Lengths

Zwick, Uri

doi:10.1007/978-3-540-30551-4_78

Cited by 27 publications

(27 citation statements)

References 24 publications

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“…The respective methods, such as ones of Strassen [16] or Coppersmith and Winograd [17], are inapplicable for obtaining the distance product, since they imply an operation inverse to addition. Another approach, proposed by Fredman [4], would be expensive to implement for larger matrices [10]. The size of the exponentiated matrix amounts to one-fourth of the size of the cost matrix, whereas some of the alternative methods for bipartite graphs (e.g., Chin-Wen and Chang [11]) achieve their acceleration on the cost of additional space proportional to the size of the cost matrix.…”

Section: Discussionmentioning

confidence: 99%

“…Nevertheless, if negative cycles exist, the Floyd-Warshall algorithm and also the subsequent algorithm can be used to detect them. The approach to be presented is a distance product APSP method known since the late 1950's [12] and widely considered in literature [7,9,10]. This method is based on the distance matrix multiplication.…”

Section: +1mentioning

confidence: 99%

“…A detailed survey of the methods that were developed so far can be found in Dragan [9] and Zwick [10]. With the progress in application areas like networking or logistics, the need to solve the APSP problem for specific classes of graphs has increased.…”

Section: Introductionmentioning

confidence: 99%

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An all-pairs shortest path algorithm for bipartite graphs

Torgasin

Zimmermann

2013

Open Computer Science

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Bipartite graphs are widely used for modeling of complex structures in biology, engineering, and computer science. The search for shortest paths in such structures is a highly demanded procedure that requires optimization. This paper presents a variant of the all-pairs shortest path algorithm for bipartite graphs. The method is based on the distance matrix product and improves the general algorithm by exploiting the graph topology. The space complexity is reduced by a factor of at least four and the time complexity decreased by almost an order of magnitude when compared with the basic APSP algorithm.

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Section: Discussionmentioning

confidence: 99%

Section: +1mentioning

confidence: 99%

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An all-pairs shortest path algorithm for bipartite graphs

Torgasin

Zimmermann

2013

Open Computer Science

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“…Since then, there have been some more progresses such as O(n 3 (log log n)/ log n) 5/7 ) [9] and O(n 3 (log log n) 2 / log n) [15], and O(n 3 log log n/ log n) [16]. Recently, algorithms with complexity O(n 3 √ log log n / log n) [18], O(n 3 (log log n/ log n) 5/4 ) [10], O(n 3 (log log n) 3 / log 2 n)) [4], etc., appeared.…”

Section: Introductionmentioning

confidence: 99%

Efficient Algorithms for the 2-Center Problems

Takaoka

2010

Computational Science and Its Applications – ICCSA 2010

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Abstract. This paper achieves O(n 3 log log n/ log n) time for the 2-center problems on a directed graph with non-negative edge costs under the conventional RAM model where only arithmetic operations, branching operations, and random accessibility with O(log n) bits are allowed. Here n is the number of vertices. This is a slight improvement on the best known complexity of those problems, which is O(n 3 ). We further show that when the graph is with unit edge costs, one of the 2-center problems can be solved in O(n 2.575 ) time.

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“…We describe two techniques that improve this time complexity to O(n 3 ) for K n 1:5 = ffiffiffiffiffiffiffiffiffi ffi log n p and even subcubic for smaller K. The first is based on the sampling technique and provides a subroutine to the second solution. With advanced algorithms for DMM [3,16,17], the second reduces the complexity to subcubic.…”

Section: Introductionmentioning

confidence: 99%

Improved Algorithms for the K-Maximum Subarray Problem

Bae

Takaoka

2005

The Computer Journal

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The maximum subarray problem is to find the contiguous array elements having the largest possible sum. We extend this problem to find K maximum subarrays. For general K maximum subarrays where overlapping is allowed, Bengtsson and Chen presented OðminfK + n log 2 n‚ n ffiffiffi ffi K p gÞ time algorithm for one-dimensional case, which finds unsorted subarrays. Our algorithm finds K maximum subarrays in sorted order with improved complexity of O ((n + K ) log K ). For the twodimensional case, we introduce two techniques that establish O(n 3 ) and subcubic time.

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A Slightly Improved Sub-cubic Algorithm for the All Pairs Shortest Paths Problem with Real Edge Lengths

Cited by 27 publications

References 24 publications

An all-pairs shortest path algorithm for bipartite graphs

An all-pairs shortest path algorithm for bipartite graphs

Efficient Algorithms for the 2-Center Problems

Improved Algorithms for the K-Maximum Subarray Problem

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