Proving relative lower bounds for incremental algorithms

Berman, A. Michael; Paull, Marvin C.; Ryder, Barbara G.

doi:10.1007/bf00259471

Cited by 15 publications

(13 citation statements)

References 12 publications

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“…Given two non-negative functions f (n) and g(n), f (n) is said to dominate g(n) if: [2] gives a general procedure for deriving the IRLB for a problem. We briefly describe this procedure here.…”

Section: Dominating Functionmentioning

confidence: 99%

“…We use the theory given in [2] to prove the IRLBs of the first three problems mentioned in the previous section.…”

Section: Relative Lower Roundsmentioning

confidence: 99%

“…Let us state the main IRLB theorem given in [2]. Here init ( I ) denotes the time taken for the initial preprocessing and computation of the initial history for the problem.…”

Section: Dominating Functionmentioning

confidence: 99%

See 2 more Smart Citations

The complexity of certain incremental code generation problems

Venugopal¹,

Srikant²

1999

International Journal of Computer Mathematics

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Section: Dominating Functionmentioning

confidence: 99%

“…We use the theory given in [2] to prove the IRLBs of the first three problems mentioned in the previous section.…”

Section: Relative Lower Roundsmentioning

confidence: 99%

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The complexity of certain incremental code generation problems

Venugopal¹,

Srikant²

1999

International Journal of Computer Mathematics

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“…This is necessary to obtaining a bounded algorithm for all dynamic graph problems we are aware of. The ideas of incremental complexity were developed over several previous works [Berman 1992;Ramalingam and Reps 1996;Ramalingam 1996] and there are many examples of its use (e.g., [Reps 1982;Alpern et al 1990;Reps et al 1986;Wirn 1993;Frigioni et al 1994;Yeh 1983;Ramalingam 1996]). …”

Section: Related Workmentioning

confidence: 99%

A dynamic topological sort algorithm for directed acyclic graphs

Pearce

2007

ACM J. Exp. Algorithmics

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We consider the problem of maintaining the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and, although this has inferior time complexity compared with the best previously known result, we find that its simplicity leads to better performance in practice. In addition, we provide an empirical comparison against the three main alternatives over a large number of random DAGs. The results show our algorithm is the best for sparse digraphs and only a constant factor slower than the best on dense digraphs.

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“…However, for incremental algorithms, as pointed out in [1] and [15], such analysis is not as informative as using the size of the changes in the input and output. For example, for some problems no incremental algorithms exist that have asymptotically better worst-case runtime than performing the computation from scratch [2], [15].…”

Section: Measures Of Runtime Complexity In Incrementalmentioning

confidence: 99%

Solving Systems of Difference Constraints Incrementally with Bidirectional Search

Zhou

Müller

2004

Algorithmica

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Abstract. We propose an incremental algorithm for the problem of maintaining systems of difference constraints. As a difference from the unidirectional approach of Ramalingam et al. [16], it employs bidirectional search, which is similar to that of Alpern et al. [1], and has a bounded runtime complexity in the worst case in terms of the size of changes. The major challenge is how to update the solution efficiently after the bidirectional search discovers a region that needs changes. Experimental results show that our approach is much faster in runtime and generates much smaller changes than the algorithm in [16]. We also perform an experimental study on the edge value heuristic [1] and results show that a simpler method may be faster in practice.

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Proving relative lower bounds for incremental algorithms

Cited by 15 publications

References 12 publications

The complexity of certain incremental code generation problems

The complexity of certain incremental code generation problems

A dynamic topological sort algorithm for directed acyclic graphs

Solving Systems of Difference Constraints Incrementally with Bidirectional Search

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