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A '''kinetic minimum spanning tree''' is a [[kinetic data structure]] that maintains the [[minimum spanning tree]] (MST) of a graph whose edge weights are changing as a continuous function of time. | |||
== General case == | |||
The most efficient known data structure for the general case uses a [[kinetic sorted list]] to store the edge weights, and a standard [[minimum spanning tree#Algorithms|MST algorithm]] to compute the MST given the sorted edge weights. This data structure must process <math>O(n^2)</math> events, developing a more [[kinetic data structure#Performance|efficient]] data structure remains an open problem.<ref name="lecture"/> | |||
== H-minor-free graphs == | |||
Agarwal ''et al.'' developed a data structure that maintains the MST for a graph belonging to a [[Minor-closed_graph_family#Minor-closed_graph_families|minor closed family]]. It uses the idea of a "swap", calculating the amount by which the weight of the MST would increase if some edge in the tree {{math|<var>e</var>}} was replaced by an edge {{math|<var>f</var>}} outside the tree such that the circle induced by {{math|<var>f</var>}} in the tree contains {{math|<var>e</var>}}. Maintaining the tree is then equivalent to finding and swapping the next pair for which this quantity becomes negative. This data structure considers the [[Duality (projective geometry)|dual]] view of the graph, and then [[divide and conquer paradigm|divides]] based on Frederickson's restricted partitions <ref name="frederickson"/> to make this efficient. It results in a total run time <math>O(pn^{\frac{1}{2}}\log^{\frac{3}{2}}n)</math> if <math>p</math> insertions or deletions are made, or <math>O(n^{\frac{19}{12}}\log^{\frac{3}{2}}n)</math> if only weight changes are allowed. These deterministic bounds are slightly improved if randomization is allowed. | |||
== References == | |||
{{Reflist|refs= | |||
<ref name="lecture"> | |||
{{cite video | url=http://courses.csail.mit.edu/6.851/spring12/lectures/L04.html | title=MIT 6.851 Advanced Data Structures, lecture video | people=Demaine, Erik D.}} | |||
</ref> | |||
<ref name="frederickson"> | |||
{{cite journal | title=Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees | author=Frederickson, G. N. |journal=SIAM Journal of Computing | year=1997 | pages=484–538}} | |||
</ref> | |||
}} | |||
==Further reading== | |||
{{cite conference | url=http://www.ics.uci.edu/~eppstein/pubs/AgaEppGui-FOCS-98.pdf | title=Parametric and Kinetic Minimum Spanning Trees | accessdate=May 19, 2012 | author=Agarwal, Pankaj; Eppstein, David; Guibas, Leonidas J.; Henzinger, Monika R. | year=1998 | conference=FOCS}} | |||
<!--- Categories ---> | |||
[[Category:Articles created via the Article Wizard]] | |||
[[Category:Kinetic data structures]] | |||
[[Category:Spanning tree]] | |||
Revision as of 15:46, 9 January 2014
A kinetic minimum spanning tree is a kinetic data structure that maintains the minimum spanning tree (MST) of a graph whose edge weights are changing as a continuous function of time.
General case
The most efficient known data structure for the general case uses a kinetic sorted list to store the edge weights, and a standard MST algorithm to compute the MST given the sorted edge weights. This data structure must process events, developing a more efficient data structure remains an open problem.[1]
H-minor-free graphs
Agarwal et al. developed a data structure that maintains the MST for a graph belonging to a minor closed family. It uses the idea of a "swap", calculating the amount by which the weight of the MST would increase if some edge in the tree Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.
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A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.
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This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.
A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.
If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.
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References
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Further reading
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