Generating the Acyclic Orientations of a Graph

Squire, Matthew B.

doi:10.1006/jagm.1997.0891

Cited by 18 publications

(27 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The algorithm proposed in [12] requires no more than logarithmic amortized time per downset generated (c.f. [11]). …”

Section: Enumerating the Augmentationsmentioning

confidence: 93%

“…Let P be an order, e s e t a passive pair in P, e i e j an incomparable pair in P +e s e t and e k ∈ E. Then e k ∈ A ij (P + e s e t )\A ij (P ) if and only if e s = e k , e t = e i and e k e j ∈ I (P ), or (11) e s = e j , e j = e k and e i e k ∈ I (P ).…”

Section: Lemmamentioning

confidence: 98%

“…For each linear extension L of P , compute all lexicographic augmentations, relative to (L, L ), using (3)-(4). Again, the downsets S i can be generated with one of the algorithms described in [2,[11][12][13]. There is no difficulty to implement this method in time O(n 2 ).…”

Section: Enumerating the Augmentationsmentioning

confidence: 99%

See 2 more Smart Citations

On extensions, linear extensions, upsets and downsets of ordered sets

Corrêa

Szwarcfiter

2005

Discrete Mathematics

View full text Add to dashboard Cite

We consider the problem of characterizing the set (P ) of all extensions of an order P on a set of elements E, where |E| = n, |P | = m and is the number of extensions of the order. Initially, we describe two distinct characterizations of (P ). The first characterization is a one-to-one correspondence between extensions of P and pairs of upsets and downsets of certain suborders of P . The second one characterizes the extensions of P in terms of linear extensions and sequences of downsets. Both characterizations lead to algorithms that generate all the extensions of P . Further, we discuss the notion of passive pairs of an order. Based on it, we describe a third characterization of (P ) and an algorithm that generates all the extensions of P in O(n) amortized time per extension.

show abstract

“…The algorithm proposed in [12] requires no more than logarithmic amortized time per downset generated (c.f. [11]). …”

Section: Enumerating the Augmentationsmentioning

confidence: 93%

Section: Lemmamentioning

confidence: 98%

See 1 more Smart Citation

On extensions, linear extensions, upsets and downsets of ordered sets

Corrêa

Szwarcfiter

2005

Discrete Mathematics

View full text Add to dashboard Cite

show abstract

“…Due to the one-to-one correspondence between interval colorings and acyclic orientations [Golumbic 2004], enumerating acyclic orientations for a given graph is another way to solve the interval coloring problem. Squire [1998] presented the first algorithm to generate all the acyclic orientations of an arbitrary graph. Barbosa and Szwarcfiter [1999] proposed another algorithm with lower complexity.…”

Section: Related Workmentioning

confidence: 99%

Comparability Graph Coloring for Optimizing Utilization of Software-Managed Stream Register Files for Stream Processors

Yang

Wang

Xue

et al. 2012

ACM Trans. Archit. Code Optim.

View full text Add to dashboard Cite

The stream processors represent a promising alternative to traditional cache-based general-purpose processors in achieving high performance in stream applications (media and some scientific applications). In a stream programming model for stream processors, an application is decomposed into a sequence of kernels operating on streams of data. During the execution of a kernel on a stream processor, all streams accessed must be communicated through a non-bypassing softwaremanaged on-chip memory, the SRF (Stream Register File). Optimizing utilization of the scarce on-chip memory is crucial for good performance. The key insight is that the interference graphs (IGs) formed by the streams in stream applications tend to be comparability graphs or decomposable into a set of comparability graphs. We present a compiler algorithm for finding optimal or near-optimal colorings, i.e., SRF allocations in stream IGs, by computing a maximum spanning forest of the sub-IG formed by long live ranges, if necessary. Our experimental results validate the optimality and near-optimality of our algorithm by comparing it with an ILP solver, and show that our algorithm yields improved SRF utilization over the First-Fit bin-packing algorithm, the best in the literature.

show abstract

“…A naive solution to Problem 1 uses the fact that enumeration algorithms exist for listing acyclic orientations [2,13]. It enumerates the cyclic orientations by difference, namely, by enumerating all the 2 m possible edge orientations and removing the α acyclic ones.…”

Section: Introductionmentioning

confidence: 99%

Enumerating Cyclic Orientations of a Graph

Conte¹,

Grossi²,

Marino³

et al. 2016

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set; it is cyclic otherwise. As far as we know, only the enumeration of acyclic orientations has been addressed in the literature. In this paper, we pose the problem of efficiently enumerating all the cyclic orientations of an undirected connected graph with n vertices and m edges, observing that it cannot be solved using algorithmic techniques previously employed for enumerating acyclic orientations. We show that the problem is of independent interest from both combinatorial and algorithmic points of view, and that each cyclic orientation can be listed withÕ(m) delay time. Space usage is O(m) with an additional setup cost of O(n 2 ) time before the enumeration begins, or O(mn) with a setup cost ofÕ(m) time.

show abstract

Generating the Acyclic Orientations of a Graph

Cited by 18 publications

References 17 publications

On extensions, linear extensions, upsets and downsets of ordered sets

On extensions, linear extensions, upsets and downsets of ordered sets

Comparability Graph Coloring for Optimizing Utilization of Software-Managed Stream Register Files for Stream Processors

Enumerating Cyclic Orientations of a Graph

Contact Info

Product

Resources

About