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Depth-First Search and Linear Graph Algorithms
- R. Tarjan
- MathematicsSIAM journal on computing (Print)
- 1 June 1972
The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components…
Amortized efficiency of list update and paging rules
This article shows that move-to-front is within a constant factor of optimum among a wide class of list maintenance rules, and analyzes the amortized complexity of LRU, showing that its efficiency differs from that of the off-line paging rule by a factor that depends on the size of fast memory.
Fibonacci heaps and their uses in improved network optimization algorithms
Using F-heaps, a new data structure for implementing heaps that extends the binomial queues proposed by Vuillemin and studied further by Brown, the improved bound for minimum spanning trees is the most striking.
A new approach to the maximum flow problem
By incorporating the dynamic tree data structure of Sleator and Tarjan, a version of the algorithm running in O(nm log(n'/m)) time on an n-vertex, m-edge graph is obtained, as fast as any known method for any graph density and faster on graphs of moderate density.
Self-adjusting binary search trees
The splay tree, a self-adjusting form of binary search tree, is developed and analyzed and is found to be as efficient as balanced trees when total running time is the measure of interest.
A Separator Theorem for Planar Graphs
Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more…
A data structure for dynamic trees
An O(mn log n)-time algorithm is obtained to find a maximum flow in a network of n vertices and m edges, beating by a factor of log n the fastest algorithm previously known for sparse graphs.
Algorithmic Aspects of Vertex Elimination on Graphs
A graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric positive definite systems of linear equations is considered, and it is conjecture that the problem of finding a minimum ordering is NP-complete.
Data structures and network algorithms
- R. Tarjan
- Computer ScienceCBMS-NSF Regional Conference Series in Applied…
This paper presents a meta-trees tree model that automates the very labor-intensive and therefore time-heavy and therefore expensive process of manually selecting trees to grow in a graph.
Three Partition Refinement Algorithms
This work presents improved partition refinement algorithms for three problems: lexicographic sorting, relational coarsest partition, and double lexical ordering that uses a new, efficient method for unmerging two sorted sets.