Balding–Nichols model

Task systems are mathematical objects used to model the set of possible configuration of online algorithms. They were introduced by Borodin, Linial and Saks (1992) to model a variety of online problems. A task system determines a set of states and costs to change states. Task systems obtain as input a sequence of requests such that each request assigns processing times to the states. The objective of an online algorithm for task systems is to create a schedule that minimizes the overall cost incurred due to processing the tasks with respect to the states and due to the cost to change states.

If the cost function to change states is a metric, the task system is a metrical task system (MTS). This is the most common type of task systems. Metrical task systems generalize online problems such as paging, list accessing, and the k-server problem (in finite spaces).

Formal Definition

A task system is a pair $(S,d)$ where $S=\{s_1,s_2,\dots ,s_n\}$ is a set of states and $d:S\times S\to \mathbb{ℝ}$ is a distance function. If $d$ is a metric, $(S,d)$ is a metrical task system. An input to the task system is a sequence $\sigma =T_1,T_2,\dots ,T_l$ such that for each $i$, $T_i$ is a vector of $n$ non-negative entries that determine the processing costs for the $n$ states when processing the $i$th task.

An algorithm for the task system produces a schedule $\pi$ that determines the sequence of states. For instance, $\pi (i)=s_j$ means that the $i$th task $T_i$ is run in state $s_j$. The processing cost of a schedule is $\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}(\pi ,\sigma )=\sum _{i=1}^{l}d(\pi (i-1),\pi (i))+T_i(\pi (i)).$

The objective of the algorithm is to find a schedule such that the cost is minimized.

Known Results

As usual for online problems, the most common measure to analyze algorithms for metrical task systems is the competitive analysis, where the performance of an online algorithm is compared to the performance of an optimal offline algorithm. For deterministic online algorithms, there is a tight bound $2n-1$ on the competitive ratio due to Borodin et al. (1992).

For randomized online algorithms, the competitive ratio is lower bounded by $\mathrm{\Omega }(\log n/\log \log n)$ and upper bounded by $O({\log }^{2}n\log \log n)$. The lower bound is due to Bartal et al. (2006,2005). The upper bound is due to Fiat and Mendel (2003) who improved upon a result of Bartal et al. (1997).

There are many results for various types of restricted metrics.

See also

• Adversary model
• Competitive analysis
• K-server problem
• Online algorithm
• Page replacement algorithm
• Real-time computing

References

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  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
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  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
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