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  • Practical rules for premature optimization

    - by DougW
    It seems that the phrase "Premature Optimization" is the buzz-word of the day. For some reason, iphone programmers in particular seem to think of avoiding premature optimization as a pro-active goal, rather than the natural result of simply avoiding distraction. The problem is, the term is beginning to be applied more and more to cases that are completely inappropriate. For example, I've seen a growing number of people say not to worry about the complexity of an algorithm, because that's premature optimization (eg http://stackoverflow.com/questions/2190275/help-sorting-an-nsarray-across-two-properties-with-nssortdescriptor/2191720#2191720). Frankly, I think this is just laziness, and appalling to disciplined computer science. But it has occurred to me that maybe considering the complexity and performance of algorithms is going the way of assembly loop unrolling, and other optimization techniques that are now considered unnecessary. What do you think? Are we at the point now where deciding between an O(n^n) and O(n!) complexity algorithm is irrelevant? What about O(n) vs O(n*n)? What do you consider "premature optimization"? What practical rules do you use to consciously or unconsciously avoid it? This is a bit vague, but I'm curious to hear other peoples' opinions on the topic.

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  • SQL SERVER – Generate Report for Index Physical Statistics – SSMS

    - by pinaldave
    Few days ago, I wrote about SQL SERVER – Out of the Box – Activity and Performance Reports from SSSMS (Link). A user asked me a question regarding if we can use similar reports to get the detail about Indexes. Yes, it is possible to do the same. There are similar type of reports are available at Database level, just like those available at the Server Instance level. You can right click on Database name and click Reports. Under Standard Reports, you will find following reports. Disk Usage Disk Usage by Top Tables Disk Usage by Table Disk Usage by Partition Backup and Restore Events All Transactions All Blocking Transactions Top Transactions by Age Top Transactions by Blocked Transactions Count Top Transactions by Locks Count Resource Locking Statistics by Objects Object Execute Statistics Database Consistency history Index Usage Statistics Index Physical Statistics Schema Change history User Statistics Select the Reports with name Index Physical Statistics. Once click, a report containing all the index names along with other information related to index will be visible, e.g. Index Type and number of partitions. One column that caught my interest was Operation Recommended. In some place, it suggested that index needs to be rebuilt. It is also possible to click and expand the column of partitions and see additional details about index as well. DBA and Developers who just want to have idea about how your index is and its physical statistics can use this tool. Click to Enlarge Note: Please note that I will rebuild my indexes just because this report is recommending it. There are many other parameters you need to consider before rebuilding indexes. However, this tool gives you the accurate stats of your index and it can be right away exported to Excel or PDF writing by clicking on the report. Reference : Pinal Dave (http://blog.SQLAuthority.com) Filed under: Pinal Dave, SQL, SQL Authority, SQL Index, SQL Optimization, SQL Performance, SQL Query, SQL Server, SQL Server Management Studio, SQL Tips and Tricks, SQL Utility, T SQL, Technology

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  • SQL SERVER – Subquery or Join – Various Options – SQL Server Engine knows the Best

    - by pinaldave
    This is followup post of my earlier article SQL SERVER – Convert IN to EXISTS – Performance Talk, after reading all the comments I have received I felt that I could write more on the same subject to clear few things out. First let us run following four queries, all of them are giving exactly same resultset. USE AdventureWorks GO -- use of = SELECT * FROM HumanResources.Employee E WHERE E.EmployeeID = ( SELECT EA.EmployeeID FROM HumanResources.EmployeeAddress EA WHERE EA.EmployeeID = E.EmployeeID) GO -- use of in SELECT * FROM HumanResources.Employee E WHERE E.EmployeeID IN ( SELECT EA.EmployeeID FROM HumanResources.EmployeeAddress EA WHERE EA.EmployeeID = E.EmployeeID) GO -- use of exists SELECT * FROM HumanResources.Employee E WHERE EXISTS ( SELECT EA.EmployeeID FROM HumanResources.EmployeeAddress EA WHERE EA.EmployeeID = E.EmployeeID) GO -- Use of Join SELECT * FROM HumanResources.Employee E INNER JOIN HumanResources.EmployeeAddress EA ON E.EmployeeID = EA.EmployeeID GO Let us compare the execution plan of the queries listed above. Click on image to see larger image. It is quite clear from the execution plan that in case of IN, EXISTS and JOIN SQL Server Engines is smart enough to figure out what is the best optimal plan of Merge Join for the same query and execute the same. However, in the case of use of Equal (=) Operator, SQL Server is forced to use Nested Loop and test each result of the inner query and compare to outer query, leading to cut the performance. Please note that here I no mean suggesting that Nested Loop is bad or Merge Join is better. This can very well vary on your machine and amount of resources available on your computer. When I see Equal (=) operator used in query like above, I usually recommend to see if user can use IN or EXISTS or JOIN. As I said, this can very much vary on different system. What is your take in above query? I believe SQL Server Engines is usually pretty smart to figure out what is ideal execution plan and use it. Reference: Pinal Dave (http://blog.SQLAuthority.com) Filed under: Pinal Dave, SQL, SQL Authority, SQL Joins, SQL Optimization, SQL Performance, SQL Query, SQL Scripts, SQL Server, SQL Tips and Tricks, T SQL, Technology

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  • SQL SERVER – Subquery or Join – Various Options – SQL Server Engine Knows the Best – Part 2

    - by pinaldave
    This blog post is part 2 of the earlier written article SQL SERVER – Subquery or Join – Various Options – SQL Server Engine knows the Best by Paulo R. Pereira. Paulo has left excellent comment to earlier article once again proving the point that SQL Server Engine is smart enough to figure out the best plan itself and uses the same for the query. Let us go over his comment as he has posted. “I think IN or EXISTS is the best choice, because there is a little difference between ‘Merge Join’ of query with JOIN (Inner Join) and the others options (Left Semi Join), and JOIN can give more results than IN or EXISTS if the relationship is 1:0..N and not 1:0..1. And if I try use NOT IN and NOT EXISTS the query plan is different from LEFT JOIN too (Left Anti Semi Join vs. Left Outer Join + Filter). So, I found a case where EXISTS has a different query plan than IN or ANY/SOME:” USE AdventureWorks GO -- use of SOME SELECT * FROM HumanResources.Employee E WHERE E.EmployeeID = SOME ( SELECT EA.EmployeeID FROM HumanResources.EmployeeAddress EA UNION ALL SELECT EA.EmployeeID FROM HumanResources.EmployeeDepartmentHistory EA ) -- use of IN SELECT * FROM HumanResources.Employee E WHERE E.EmployeeID IN ( SELECT EA.EmployeeID FROM HumanResources.EmployeeAddress EA UNION ALL SELECT EA.EmployeeID FROM HumanResources.EmployeeDepartmentHistory EA ) -- use of EXISTS SELECT * FROM HumanResources.Employee E WHERE EXISTS ( SELECT EA.EmployeeID FROM HumanResources.EmployeeAddress EA UNION ALL SELECT EA.EmployeeID FROM HumanResources.EmployeeDepartmentHistory EA ) When looked into execution plan of the queries listed above indeed we do get different plans for queries and SQL Server Engines creates the best (least cost) plan for each query. Click on image to see larger images. Thanks Paulo for your wonderful contribution. Reference : Pinal Dave (http://blog.SQLAuthority.com) Filed under: Pinal Dave, Readers Contribution, SQL, SQL Authority, SQL Joins, SQL Optimization, SQL Performance, SQL Query, SQL Scripts, SQL Server, SQL Tips and Tricks, T SQL, Technology

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  • SQLAuthority News – A Successful Performance Tuning Seminar at Pune – Dec 4-5, 2010

    - by pinaldave
    This is report to my third of very successful seminar event on SQL Server Performance Tuning. SQL Server Performance Tuning Seminar in Colombo was oversubscribed with total of 35 attendees. You can read the details over here SQLAuthority News – SQL Server Performance Optimizations Seminar – Grand Success – Colombo, Sri Lanka – Oct 4 – 5, 2010. SQL Server Performance Tuning Seminar in Hyderabad was oversubscribed with total of 25 attendees. You can read the details over here SQL SERVER – A Successful Performance Tuning Seminar – Hyderabad – Nov 27-28, 2010. The same Seminar was offered in Pune on December 4,-5, 2010. We had another successful seminar with lots of performance talk. This seminar was attended by 30 attendees. The best part of the seminar was that along with the our agenda, we have talked about following very interesting concepts. Deadlocks Detection and Removal Dynamic SQL and Inline Code SQL Optimizations Multiple OR conditions and performance tuning Dynamic Search Condition Building and Improvement Memory Cache and Improvement Bottleneck Detections – Memory, CPU and IO Beginning Performance Tuning on Production Parametrization Improving already Super Fast Queries Convenience vs. Performance Proper way to create Indexes Hints and Disadvantages I had great time doing the seminar and sharing my performance tricks with all. The highlight of this seminar was I have explained the attendees, how I begin doing performance tuning when I go for Performance Tuning Consultations.   Pinal Dave at SQL Performance Tuning Seminar SQL Server Performance Tuning Seminar Pinal Dave at SQL Performance Tuning Seminar Pinal Dave at SQL Performance Tuning Seminar SQL Server Performance Tuning Seminar SQL Server Performance Tuning Seminar This seminar series are 100% demo oriented and no usual PowerPoint talk. They are created from my experiences of various organizations for performance tuning. I am not planning any more seminar this year as it was great but I am booked currently for next 60 days at various performance tuning engagements. Reference: Pinal Dave (http://blog.sqlauthority.com) Filed under: Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Server, SQL Tips and Tricks, SQL Training, SQLAuthority News, T SQL, Technology

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  • SQL SERVER – Activity Monitor and Performance Issue

    - by pinaldave
    We had wonderful SQLAuthority News – Community Tech Days – December 11, 2010 event yesterday. After the event, we had meeting among Jacob Sebastian, Vinod Kumar, Rushabh Mehta and myself. We all were sharing our experience about performance tuning consultations. During the conversation, Jacob has shared wonderful story of his recent observation. The story is very small but the moral of the story is very important. The story is about a client, who had continuously performance issues. Client used Activity Monitor (Read More: SQL SERVER – 2008 – Location of Activity Monitor – Where is SQL Serve Activity Monitor Located) to check the performance issues. The pattern of the performance issues was very much common all the time. Every time, after a while the computer stopped responding. After doing in-depth performance analysis, Jacob realized that client once opened activity monitor never closed it. The same activity monitor itself is very expensive process. The tool, which helped to debug the performance issues, also helped (negatively) to bring down the server. After closing the activity monitor which was open for long time, the server did not have performance issues. Moral of the story: Activity Monitor is great tool but use it with care and close it when not needed. Reference: Pinal Dave (http://blog.SQLAuthority.com) Filed under: Best Practices, Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Server, SQL Tips and Tricks, T SQL, Technology

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  • SQLAuthority News – Statistics and Best Practices – Virtual Tech Days – Nov 22, 2010

    - by pinaldave
    I am honored that I have been invited to speak at Virtual TechDays on Nov 22, 2010 by Microsoft. I will be speaking on my favorite subject of Statistics and Best Practices. This exclusive online event will have 80 deep technical sessions across 3 days – and, attendance is completely FREE. There are dedicated tracks for Architects, Software Developers/Project Managers, Infrastructure Managers/Professionals and Enterprise Developers. So, REGISTER for this exclusive online event TODAY. Statistics and Best Practices Timing: 11:45am-12:45pm Statistics are a key part of getting solid performance. In this session we will go over the basics of the statistics and various best practices related to Statistics. We will go over various frequently asked questions like a) when to update statistics, b) different between sync and async update of statistics c) best method to update statistics d) optimal interval of updating statistics. We will also discuss the pros and cons of the statistics update. This session is for all of you – whether you’re a DBA or developer! You can register for this event over here. If you have never attended my session on this subject I strongly suggest that you attend the event as this is going to be very interesting conversation between us. If you have attended this session earlier, this will contain few new information which will for sure interesting to share with all. Reference: Pinal Dave (http://blog.sqlauthority.com) Filed under: MVP, Pinal Dave, SQL, SQL Authority, SQL Joins, SQL Optimization, SQL Performance, SQL Query, SQL Server, SQL Tips and Tricks, SQLAuthority News, T SQL, Technology Tagged: SQL Statistics, Statistics

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  • SQL SERVER – What is Page Life Expectancy (PLE) Counter

    - by pinaldave
    During performance tuning consultation there are plenty of counters and values, I often come across. Today we will quickly talk about Page Life Expectancy counter, which is commonly known as PLE as well. You can find the value of the PLE by running following query. SELECT [object_name], [counter_name], [cntr_value] FROM sys.dm_os_performance_counters WHERE [object_name] LIKE '%Manager%' AND [counter_name] = 'Page life expectancy' The recommended value of the PLE counter is 300 seconds. I have seen on busy system this value to be as low as even 45 seconds and on unused system as high as 1250 seconds. Page Life Expectancy is number of seconds a page will stay in the buffer pool without references. In simple words, if your page stays longer in the buffer pool (area of the memory cache) your PLE is higher, leading to higher performance as every time request comes there are chances it may find its data in the cache itself instead of going to hard drive to read the data. Now check your system and post back what is this counter value for you during various time of the day. Is this counter any way relates to performance issues for your system? Note: There are various other counters which are important to discuss during the performance tuning and this counter is not everything. Reference: Pinal Dave (http://blog.SQLAuthority.com) Filed under: Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Scripts, SQL Server, SQL Tips and Tricks, SQLServer, T SQL, Technology

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  • SQL SERVER – Find Most Expensive Queries Using DMV

    - by pinaldave
    The title of this post is what I can express here for this quick blog post. I was asked in recent query tuning consultation project, if I can share my script which I use to figure out which is the most expensive queries are running on SQL Server. This script is very basic and very simple, there are many different versions are available online. This basic script does do the job which I expect to do – find out the most expensive queries on SQL Server Box. SELECT TOP 10 SUBSTRING(qt.TEXT, (qs.statement_start_offset/2)+1, ((CASE qs.statement_end_offset WHEN -1 THEN DATALENGTH(qt.TEXT) ELSE qs.statement_end_offset END - qs.statement_start_offset)/2)+1), qs.execution_count, qs.total_logical_reads, qs.last_logical_reads, qs.total_logical_writes, qs.last_logical_writes, qs.total_worker_time, qs.last_worker_time, qs.total_elapsed_time/1000000 total_elapsed_time_in_S, qs.last_elapsed_time/1000000 last_elapsed_time_in_S, qs.last_execution_time, qp.query_plan FROM sys.dm_exec_query_stats qs CROSS APPLY sys.dm_exec_sql_text(qs.sql_handle) qt CROSS APPLY sys.dm_exec_query_plan(qs.plan_handle) qp ORDER BY qs.total_logical_reads DESC -- logical reads -- ORDER BY qs.total_logical_writes DESC -- logical writes -- ORDER BY qs.total_worker_time DESC -- CPU time You can change the ORDER BY clause to order this table with different parameters. I invite my reader to share their scripts. Reference: Pinal Dave (http://blog.SQLAuthority.com) Filed under: Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Scripts, SQL Server, SQL Tips and Tricks, SQLAuthority News, SQLServer, T SQL, Technology Tagged: SQL DMV

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  • SQLAuthority News – 18 Seconds of Fame – My PASS Experience

    - by pinaldave
    Happy Holidays to All of YOU! Life is full of little and happy surprises. I think Christmas and Santa are based on it. I just received very interesting email earlier today, I had no idea about it. Earlier this year, I had visited Seattle to attend SQLPASS – read the complete summary over here: SQLAuthority News – SQLPASS Nov 8-11, 2010-Seattle – An Alternative Look at Experience. While I was walking down, someone has stopped me and asked if they can talk to me for 15 seconds, I said yes and they had shot quick movie with mobile. The conversation was very quick and I had forgotten about it. Today I received email from one of the blog reader about it being on YouTube. Honestly, I did not know if this was ever going to be on YouTube. I am surprised and thrilled. Watch my 18 seconds fame movie. Reference: Pinal Dave (http://blog.sqlauthority.com) Filed under: About Me, Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Server, SQL Tips and Tricks, SQLAuthority Author Visit, T SQL, Technology

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  • SQL SERVER – Plan Cache and Data Cache in Memory

    - by pinaldave
    I get following question almost all the time when I go for consultations or training. I often end up providing the scripts to my clients and attendees. Instead of writing new blog post, today in this single blog post, I am going to cover both the script and going to link to original blog posts where I have mentioned about this blog post. Plan Cache in Memory USE AdventureWorks GO SELECT [text], cp.size_in_bytes, plan_handle FROM sys.dm_exec_cached_plans AS cp CROSS APPLY sys.dm_exec_sql_text(plan_handle) WHERE cp.cacheobjtype = N'Compiled Plan' ORDER BY cp.size_in_bytes DESC GO Further explanation of this script is over here: SQL SERVER – Plan Cache – Retrieve and Remove – A Simple Script Data Cache in Memory USE AdventureWorks GO SELECT COUNT(*) AS cached_pages_count, name AS BaseTableName, IndexName, IndexTypeDesc FROM sys.dm_os_buffer_descriptors AS bd INNER JOIN ( SELECT s_obj.name, s_obj.index_id, s_obj.allocation_unit_id, s_obj.OBJECT_ID, i.name IndexName, i.type_desc IndexTypeDesc FROM ( SELECT OBJECT_NAME(OBJECT_ID) AS name, index_id ,allocation_unit_id, OBJECT_ID FROM sys.allocation_units AS au INNER JOIN sys.partitions AS p ON au.container_id = p.hobt_id AND (au.TYPE = 1 OR au.TYPE = 3) UNION ALL SELECT OBJECT_NAME(OBJECT_ID) AS name, index_id, allocation_unit_id, OBJECT_ID FROM sys.allocation_units AS au INNER JOIN sys.partitions AS p ON au.container_id = p.partition_id AND au.TYPE = 2 ) AS s_obj LEFT JOIN sys.indexes i ON i.index_id = s_obj.index_id AND i.OBJECT_ID = s_obj.OBJECT_ID ) AS obj ON bd.allocation_unit_id = obj.allocation_unit_id WHERE database_id = DB_ID() GROUP BY name, index_id, IndexName, IndexTypeDesc ORDER BY cached_pages_count DESC; GO Further explanation of this script is over here: SQL SERVER – Get Query Plan Along with Query Text and Execution Count Reference: Pinal Dave (http://blog.SQLAuthority.com) Filed under: Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Scripts, SQL Server, SQL Tips and Tricks, T SQL Tagged: SQL Memory

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  • How does an optimizing compiler react to a program with nested loops?

    - by D.Singh
    Say you have a bunch of nested loops. public void testMethod() { for(int i = 0; i<1203; i++){ //some computation for(int k=2; k<123; k++){ //some computation for(int j=2; j<12312; j++){ //some computation for(int l=2; l<123123; l++){ //some computation for(int p=2; p<12312; p++){ //some computation } } } } } } When the above code reaches the stage where the compiler will try to optimize it (I believe it's when the intermediate language needs to converted to machine code?), what will the compiler try to do? Is there any significant optimization that will take place? I understand that the optimizer will break up the loops by means of loop fission. But this is only per loop isn't it? What I mean with my question is will it take any action exclusively based on seeing the nested loops? Or will it just optimize the loops one by one? If the Java VM complicates the explanation then please just assume that it's C or C++ code.

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  • algorithm for Virtual Machine(VM) Consolidation in Cloud

    - by devansh dalal
    PROBLEM: We have N physical machines(PMs) each with ram Ri, cpu Ci and a set of currently scheduled VMs each with ram requirement ri and ci respectively Moving(Migrating) any VM from one PM to other has a cost associated which depends on its ram ri. A PM with no VMs is shut down to save power. Our target is to minimize the weighted sum of (N,migration cost) by migrating some VMs i.e. minimize the number of working PMs as well as not to degrade the service level due to excessive migrations. My Approach: Brute Force approach is choosing the minimum loaded PM and try to fit its VMs to other PMs by First Fit Decreasing algorithm or we can select the victim PMs and target PMs based on their loading level and shut down victims if possible by moving their VMs to targets. I tried this Greedy approach on the Data of Baadal(IIT-D cloud) but It isn't giving promising results. I have also tried to study the Ant colony optimization for dynamic VM consolidating but was unable to understand very much. I used the links. http://dumas.ccsd.cnrs.fr/docs/00/72/52/15/PDF/Esnault.pdf http://hal.archives-ouvertes.fr/docs/00/72/38/56/PDF/RR-8032.pdf Would anyone please explain the solution or suggest any new approach for better performance soon. Thanks in advance.

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  • How to optimize a box2d simulation in action game?

    - by nathan
    I'm working on an action game and i use box2d for physics. The game use a tiled map. I have different types of body: Static ones used for tiles Dynamic ones for player and enemies Actually i tested my game with ~150 bodies and i have a 60fps constantly on my computer but not on my mobile (android). The FPS drop as the number of body increase. After having profiled the android application, i saw that the World.step took around 8ms in CPU time to execute. Here are few things to note: Not all the world is visible on screen, i use a scrolling system Enemies are constantly moving toward the player so there is alaways to force applied to their body Enemies need to collide between each others Enemies collide with tiles I also now that i can active/desactive or sleep/awake bodies. Considering the fact that only a part of the enemies are possibly displayed on screen, is there any optimizations i can do to reduce the execution time of box2d simulation? I found a guy trying an optimization based on distance of enemies from the player (link). But i seems like he just desactives far bodies (in my case, i could desactive bodies that are not visible). But my enemies need to move even when they are not visible on screen, and applying forces will not workd on inactive bodies. Should i play with sleeping bodies here? Also, enemies are composed by two fixtures and are constantly colliding with each others and with tiles but i really never need to get notified about that. Is there anything i can do to optimize this kind of scenario? Finally, am i wrong to try to run simulation at 60FPS on mobile and should i try to make it run at 30FPS?

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  • Efficient algorithm for Virtual Machine(VM) Consolidation in Cloud

    - by devansh dalal
    PROBLEM: We have N physical machines(PMs) each with ram Ri, cpu Ci and a set of currently scheduled VMs each with ram requirement ri and ci respectively Moving(Migrating) any VM from one PM to other has a cost associated which depends on its ram ri. A PM with no VMs is shut down to save power. Our target is to minimize the weighted sum of (N,migration cost) by migrating some VMs i.e. minimize the number of working PMs as well as not to degrade the service level due to excessive migrations. My Approach: Brute Force approach is choosing the minimum loaded PM and try to fit its VMs to other PMs by First Fit Decreasing algorithm or we can select the victim PMs and target PMs based on their loading level and shut down victims if possible by moving their VMs to targets. I tried this Greedy approach on the Data of Baadal(IIT-D cloud) but It isn't giving promising results. I have also tried to study the Ant colony optimization for dynamic VM consolidating but was unable to understand very much. I used the links. http://dumas.ccsd.cnrs.fr/docs/00/72/52/15/PDF/Esnault.pdf http://hal.archives-ouvertes.fr/docs/00/72/38/56/PDF/RR-8032.pdf Would anyone please clarify the solution or suggest any new approach/resources for better performance. I am basically searching for the algorithms not the physical optimizations and I also know that many commercial organizations have provided these solution but I just wanted to know more the underlying algorithms. Thanks in advance.

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  • FREE eBook: .NET Performance Testing and Optimization (Part 1)

    In this this first part of complete guide to performance profiling, Paul Glavich and Chris Farrell explain why performance testing is a good idea and walk you through everything you need to know to set up a test environment. This comprehensive guide to getting started is an essential handbook to any programmer looking to set up a .NET testing environment and get the best results out of it. Download your free copy now span.fullpost {display:none;}

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  • Silverlight: Search Engine Optimization

    - by xamlnotes
    I am doing lots of consulting on Silverlight these days. So I was looking into search enabling Sl applications. So I found this great whitepaper on this very subject. I will post more on this same subject as I get into implementing these ideas as well as some of my own I want to try out. Silverlight is really rocking the world today with more and more applications rolling out. So check out this great whitepaper to see whats cooking with SEO for yours. http://www.silverlight.net/learn/whitepapers/seo-for-silverlight/

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  • Extreme Optimization – Curves (Function Mapping) Part 1

    - by JoshReuben
    Overview ·        a curve is a functional map relationship between two factors (i.e. a function - However, the word function is a reserved word). ·        You can use the EO API to create common types of functions, find zeroes and calculate derivatives - currently supports constants, lines, quadratic curves, polynomials and Chebyshev approximations. ·        A function basis is a set of functions that can be combined to form a particular class of functions.   The Curve class ·        the abstract base class from which all other curve classes are derived – it provides the following methods: ·        ValueAt(Double) - evaluates the curve at a specific point. ·        SlopeAt(Double) - evaluates the derivative ·        Integral(Double, Double) - evaluates the definite integral over a specified interval. ·        TangentAt(Double) - returns a Line curve that is the tangent to the curve at a specific point. ·        FindRoots() - attempts to find all the roots or zeroes of the curve. ·        A particular type of curve is defined by a Parameters property, of type ParameterCollection   The GeneralCurve class ·        defines a curve whose value and, optionally, derivative and integrals, are calculated using arbitrary methods. A general curve has no parameters. ·        Constructor params:  RealFunction delegates – 1 for the function, and optionally another 2 for the derivative and integral ·        If no derivative  or integral function is supplied, they are calculated via the NumericalDifferentiation  and AdaptiveIntegrator classes in the Extreme.Mathematics.Calculus namespace. // the function is 1/(1+x^2) private double f(double x) {     return 1 / (1 + x*x); }   // Its derivative is -2x/(1+x^2)^2 private double df(double x) {     double y = 1 + x*x;     return -2*x* / (y*y); }   // The integral of f is Arctan(x), which is available from the Math class. var c1 = new GeneralCurve (new RealFunction(f), new RealFunction(df), new RealFunction(System.Math.Atan)); // Find the tangent to this curve at x=1 (the Line class is derived from Curve) Line l1 = c1.TangentAt(1);

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  • SEO optimization for AJAX site and dynamic HTML canvas

    - by Christian Benincasa
    I have a site that uses AJAX to query the Last.fm database and then dynamically draws a graph of the results on an HTML canvas. In the search function, I have a command that sets window.location.hash to the search parameters. I also have a function that checks if a hash was provided in the url and if so, generates the page. For example, http://www.thenlistento.com/#!/led+zeppelin will automatically navigate to a search page for Led Zeppelin. My question is, how do optimize this set up for SEO? Can it be done at all? I've taken a look at Google Webmaster Docs and read over the hashbang protocol, but I'm not totally sure how to apply it to my situation..or even if I can at all. Any help/suggestions would be greatly appreciated. Link to the site: http://www.thenlistento.com

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