Recent results on the single-source shortest paths problem
@article{Raman1997RecentRO, title={Recent results on the single-source shortest paths problem}, author={Rajeev Raman}, journal={SIGACT News}, year={1997}, volume={28}, pages={81-87} }
We summarize the currently best known theoretical results for the single-source shortest paths problem for directed graphs with non-negative edge weights. We also point out that a recent result due to Cherkassky, Goldberg and Silverstein (1996) leads to even better time bounds for this problem than claimed by the authors.
82 Citations
Exact and Approximate Distances in Graphs - A Survey
- MathematicsESA
- 2001
We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different…
A Simple Shortest Path Algorithm with Linear Average Time
- Computer Science, MathematicsESA
- 2001
This work presents a simple shortest path algorithm that runs in linear time if the input lengths are positive and uniformly distributed, and the worst-case running time is O(m + n log C).
Undirected single-source shortest paths with positive integer weights in linear time
- Computer ScienceJACM
- 1999
A deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with positive integer weights, which avoids the sorting bottleneck by building a hierarchical bucketing structure.
Directed single-source shortest-paths in linear average-case time
- Computer Science, Mathematics
- 2001
This paper gives simple label-setting and label-correcting algorithms for arbitrary directed graphs with random real edge weights uniformly distributed in [0; 1℄] and shows that they need linear timeO(n+m) with high probability.
Shortest path algorithm with pre-calculated single link failure recovery for non-negative weighted undirected graphs
- Business, Computer Science2010 International Conference on Information and Emerging Technologies
- 2010
Initial finding and achievements to recover from a single link failure on the shortest path with optimal alternate path keeping the cost low are presented.
Undirected single source shortest paths in linear time
- Computer ScienceProceedings 38th Annual Symposium on Foundations of Computer Science
- 1997
A deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with integer weights, avoids the sorting bottle-neck by building a hierarchical bucketing structure, identifying vertex pairs that may be visited in any order.
Shortest Path Algorithms: Engineering Aspects
- Computer ScienceISAAC
- 2001
The experimental results suggest that the caliber heuristic and adaptive parameter selection give an efficient algorithm, both on typical and on hard inputs, for a wide range of arc lengths.
A New Single-Source Shortest Path Algorithm for Nonnegative Weight Graph
- Computer Science
- 2014
It is demonstrated that the proposed new single-source shortest path algorithm for nonnegative weight graph is faster than Dijkstra's algorithm using Fibonacci heap in average situation when n is large enough.
A Shortest Path Algorithm for Real-Weighted Undirected Graphs
- Computer ScienceSIAM J. Comput.
- 2005
The algorithm takes the hierarchy-based approach invented by Thorup, and, if the ratio between the maximum and minimum edge lengths is bounded by n(log n)O(1), it can solve the single-source problem in O(m + n log log n) time.
A near linear shortest path algorithm for weighted undirected graphs
- Computer Science, Business2011 IEEE Symposium on Computers & Informatics
- 2011
The presented algorithm uses Depth First Search like graph traversal during a BFS like traversal i.e. combines and take advantage of the inherent properties of the two heuristic graph search techniques so that vertex weights can be kept balanced.
References
SHOWING 1-10 OF 12 REFERENCES
Undirected single source shortest paths in linear time
- Computer ScienceProceedings 38th Annual Symposium on Foundations of Computer Science
- 1997
A deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with integer weights, avoids the sorting bottle-neck by building a hierarchical bucketing structure, identifying vertex pairs that may be visited in any order.
Heap-on-Top Priority Queues
- Computer Science
- 1996
The heap-on-top (hot) priority queue data structure that combines the multi-level bucket data structure of Denardo and Fox and a heap is introduced to obtain an O(m+n(log C) 1 3 +) expected time implementation of Dijkstra's shortest path algorithm.
Priority Queues: Small, Monotone and Trans-dichotomous
- MathematicsESA
- 1996
We consider two data-structuring problems which involve performing priority queue (pq) operations on a set of integers in the range 0..2w−1 on a unit-cost RAM with word size ω bits.
Buckets, heaps, lists, and monotone priority queues
- Computer ScienceSODA '97
- 1997
The heap-on-top (hot) priority queue data structure that combines the multilevel bucket data structure of Denardo and Fox with a heap is introduced and used to obtain an improved bound for Dijkstra's shortest path algorithm.
Sorting in linear time?
- Computer ScienceSTOC '95
- 1995
We show that a unit-cost RAM with a word length of bits can sort integers in the range in time, for arbitrary ! , a significant improvement over the bound of " # $ achieved by the fusion trees of…
Faster algorithms for the shortest path problem
- Computer ScienceJACM
- 1990
Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the <italic>radix heap</italic>, is proposed for use in this algorithm. On a network…
On RAM priority queues
- Computer ScienceSODA '96
- 1996
On a RAM, the amortized operation cost of a monotone priority queue is equivalent to the per-key cost of sorting, and the equivalence implies that the single source shortest paths problem on a graph with m edges is no harder than that of sorting m keys.
Shortest-Route Methods
- 1979
Fibonacci heaps and their uses in improved network optimization problems
- J. ACM
- 1987
Shortest-route methods: 1. Resr hlng, pvm~ng and buckets
- Oper. Res
- 1979