Comparative Pathway Annotation With Protein-Dna Interaction and Operon Information via Graph Tree Decomposition

Zhao, Jizhen; Che, Dongsheng; Cai, Liming

doi:10.1142/9789812772435_0047

Cited by 6 publications

(5 citation statements)

References 13 publications

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“…The notions of treewidth and tree decomposition have gained their attractiveness partly because many graph and network problems that are intractable (e.g., NP-hard) on arbitrary graphs become more efficiently solvable (e.g., with a linear time algorithm) when the treewidth of the input graphs is bounded by a constant. Such algorithms have been found for many combinatorial problems (see e.g., [3,6,46,60,63]), and also have been employed for problems from computational biology (see e.g., [64,65]), constraint satisfaction (see e.g., [25,36,46]), and probabilistic networks (see [49]).…”

Section: Introductionmentioning

confidence: 99%

Treewidth computations I. Upper bounds

Bodlaender¹,

Koster²

2010

Information and Computation

150

124

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For more and more applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast. This paper gives an overview of several upper bound heuristics that have been proposed and tested for the problem of determining the treewidth of a graph and finding tree decompositions. Each of the heuristics produces tree decompositions whose width is not necessarily optimal, but experiments show that many of these come often close to the exact treewidth.

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Section: Introductionmentioning

confidence: 99%

Treewidth computations I. Upper bounds

Bodlaender¹,

Koster²

2010

Information and Computation

150

124

View full text Add to dashboard Cite

show abstract

“…As a crude threshold of whether a cluster/community is localized, we consider it to be localized if it is contained in fewer bags than there are nodes in the community. 14 We apply this method using the amd heuristic.…”

Section: Connections With Good-conductance Communities Resultsmentioning

confidence: 99%

“…In particular, there are polynomial-time algorithms for solving many such problems on all graphs that have TDs whose width (defined below) is bounded from above by a constant [8,9]. These algorithms have been applied to problems in constraint satisfaction, computational biology, linear algebra, probabilistic networks, and machine learning [10,11,12,13,14,15,16,17,18].…”

Section: Preliminaries On Tree Decompositionsmentioning

confidence: 99%

Tree decompositions and social graphs

Adcock

Sullivan

Mahoney

2016

Internet Mathematics

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Recent work has established that large informatics graphs such as social and information networks have non-trivial tree-like structure when viewed at moderate size scales. Here, we present results from the first detailed empirical evaluation of the use of tree decomposition (TD) heuristics for structure identification and extraction in social graphs. Although TDs have historically been used in structural graph theory and scientific computing, we show that-even with existing TD heuristics developed for those very different areas-TD methods can identify interesting structure in a wide range of realistic informatics graphs. Our main contributions are the following: we show that TD methods can identify structures that correlate strongly with the core-periphery structure of realistic networks, even when using simple greedy heuristics; we show that the peripheral bags of these TDs correlate well with low-conductance communities (when they exist) found using local spectral computations; and we show that several types of large-scale "ground-truth" communities, defined by demographic metadata on the nodes of the network, are well-localized in the large-scale and/or peripheral structures of the TDs. Our other main contributions are the following: we provide detailed empirical results for TD heuristics on toy and synthetic networks to establish a baseline to understand better the behavior of the heuristics on more complex real-world networks; and we prove a theorem providing formal justification for the intuition that the only two impediments to low-distortion hyperbolic embedding are high tree-width and long geodesic cycles. Our results suggest future directions for improved TD heuristics that are more appropriate for realistic social graphs.

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“…Koster et al [30] studied how to use tree decomposition to solve combinatorial optimization problems. In addition, Zhao et al [31,32] published two papers that exploit tree decomposition to solve some problems about computational biology. In the area of graphical models, including knowledge representation and reasoning, probabilistic reasoning, and constraint satisfaction [33,34], all these studies focused on some graphs to represent abundant information about the real world.…”

Section: Related Workmentioning

confidence: 99%

The Treewidth of Induced Graphs of Conditional Preference Networks Is Small

Liu

2016

Information

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Conditional preference networks (CP-nets) are recently an emerging topic as a graphical model for compactly representing ordinal conditional preference relations on multi-attribute domains. As we know, the treewidth, which can decrease the solving complexity for many intractability problems, is exactly a fundamental property of a graph. Therefore, we can utilize treewidth to solve some reasoning tasks on induced graphs, such as the dominance queries on the CP-nets in the future. In this paper, we present an efficient algorithm for computing the treewidth of induced graphs of CP-nets; what we need is to make an assumption that the induced graph of a CP-net has been given. Then, we can leverage the Bucket Elimination technique to solve treewidth within polynomial time. At last, it is revealed that by our experiment, the treewidth of induced graphs of CP-nets is much smaller with regard to the number of vertices. For example, for an induced graph of CP-net with 1024 vertices, its treewidth is only 10. As far as we know, this is the first time, using the Bucket Elimination, to compute the treewidth of an induced graph of a CP-net. This approach for solving the treewidth may lay a good foundation for efficiently solving dominance queries on CP-nets in the future.

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Comparative Pathway Annotation With Protein-Dna Interaction and Operon Information via Graph Tree Decomposition

Cited by 6 publications

References 13 publications

Treewidth computations I. Upper bounds

Treewidth computations I. Upper bounds

Tree decompositions and social graphs

The Treewidth of Induced Graphs of Conditional Preference Networks Is Small

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