Randomized rounding

Randomized rounding

In computer science and operations research, randomized rounding is a widely used approach for designing and analyzing approximation algorithms. Many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). For such problems, randomized rounding can be used to design fast (polynomial time) approximation algorithms—that is, algorithms that are guaranteed to return an approximately optimal solution given any input. The basic idea of randomized rounding is to convert an optimal solution of a relaxation of the problem into an approximately-optimal solution to the original problem. The resulting algorithm is usually analyzed using the probabilistic method. == Overview == The basic approach has three steps: Formulate the problem to be solved as an integer linear program (ILP). Compute an optimal fractional solution x {\displaystyle x} to the linear programming relaxation (LP) of the ILP. Round the fractional solution x {\displaystyle x} of the LP to an integer solution x ′ {\displaystyle x'} of the ILP. (Although the approach is most commonly applied with linear programs, other kinds of relaxations are sometimes used. For example, see Goemans' and Williamson's semidefinite programming-based Max-Cut approximation algorithm.) In the first step, the challenge is to choose a suitable integer linear program. Familiarity with linear programming, in particular modelling using linear programs and integer linear programs, is required. For many problems, there is a natural integer linear program that works well, such as in the Set Cover example below. (The integer linear program should have a small integrality gap; indeed randomized rounding is often used to prove bounds on integrality gaps.) In the second step, the optimal fractional solution can typically be computed in polynomial time using any standard linear programming algorithm. In the third step, the fractional solution must be converted into an integer solution (and thus a solution to the original problem). This is called rounding the fractional solution. The resulting integer solution should (provably) have cost not much larger than the cost of the fractional solution. This will ensure that the cost of the integer solution is not much larger than the cost of the optimal integer solution. The main technique used to do the third step (rounding) is to use randomization, and then to use probabilistic arguments to bound the increase in cost due to the rounding (following the probabilistic method from combinatorics). Therein, probabilistic arguments are used to show the existence of discrete structures with desired properties. In this context, one uses such arguments to show the following: Given any fractional solution x {\displaystyle x} of the LP, with positive probability the randomized rounding process produces an integer solution x ′ {\displaystyle x'} that approximates x {\displaystyle x} according to some desired criterion. Finally, to make the third step computationally efficient, one either shows that x ′ {\displaystyle x'} approximates x {\displaystyle x} with high probability (so that the step can remain randomized) or one derandomizes the rounding step, typically using the method of conditional probabilities. The latter method converts the randomized rounding process into an efficient deterministic process that is guaranteed to reach a good outcome. == Example: the set cover problem == The following example illustrates how randomized rounding can be used to design an approximation algorithm for the set cover problem. Fix any instance ⟨ c , S ⟩ {\displaystyle \langle c,{\mathcal {S}}\rangle } of set cover over a universe U {\displaystyle {\mathcal {U}}} . === Computing the fractional solution === For step 1, let IP be the standard integer linear program for set cover for this instance. For step 2, let LP be the linear programming relaxation of IP, and compute an optimal solution x ∗ {\displaystyle x^{}} to LP using any standard linear programming algorithm. This takes time polynomial in the input size. The feasible solutions to LP are the vectors x {\displaystyle x} that assign each set s ∈ S {\displaystyle s\in {\mathcal {S}}} a non-negative weight x s {\displaystyle x_{s}} , such that, for each element e ∈ U {\displaystyle e\in {\mathcal {U}}} , x ′ {\displaystyle x'} covers e {\displaystyle e} —the total weight assigned to the sets containing e {\displaystyle e} is at least 1, that is, ∑ s ∋ e x s ≥ 1. {\displaystyle \sum _{s\ni e}x_{s}\geq 1.} The optimal solution x ∗ {\displaystyle x^{}} is a feasible solution whose cost ∑ s ∈ S c ( S ) x s ∗ {\displaystyle \sum _{s\in {\mathcal {S}}}c(S)x_{s}^{}} is as small as possible. Note that any set cover C {\displaystyle {\mathcal {C}}} for S {\displaystyle {\mathcal {S}}} gives a feasible solution x {\displaystyle x} (where x s = 1 {\displaystyle x_{s}=1} for s ∈ C {\displaystyle s\in {\mathcal {C}}} , x s = 0 {\displaystyle x_{s}=0} otherwise). The cost of this C {\displaystyle {\mathcal {C}}} equals the cost of x {\displaystyle x} , that is, ∑ s ∈ C c ( s ) = ∑ s ∈ S c ( s ) x s . {\displaystyle \sum _{s\in {\mathcal {C}}}c(s)=\sum _{s\in {\mathcal {S}}}c(s)x_{s}.} In other words, the linear program LP is a relaxation of the given set-cover problem. Since x ∗ {\displaystyle x^{}} has minimum cost among feasible solutions to the LP, the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover. === Randomized rounding step === In step 3, we must convert the minimum-cost fractional set cover x ∗ {\displaystyle x^{}} into a feasible integer solution x ′ {\displaystyle x'} (corresponding to a true set cover). The rounding step should produce an x ′ {\displaystyle x'} that, with positive probability, has cost within a small factor of the cost of x ∗ {\displaystyle x^{}} .Then (since the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover), the cost of x ′ {\displaystyle x'} will be within a small factor of the optimal cost. As a starting point, consider the most natural rounding scheme: For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( 1 , x s ∗ ) {\displaystyle \min(1,x_{s}^{})} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . With this rounding scheme, the expected cost of the chosen sets is at most ∑ s c ( s ) x s ∗ {\displaystyle \sum _{s}c(s)x_{s}^{}} , the cost of the fractional cover. This is good. Unfortunately the coverage is not good. When the variables x s ∗ {\displaystyle x_{s}^{}} are small, the probability that an element e {\displaystyle e} is not covered is about ∏ s ∋ e 1 − x s ∗ ≈ ∏ s ∋ e exp ⁡ ( − x s ∗ ) = exp ⁡ ( − ∑ s ∋ e x s ∗ ) ≈ exp ⁡ ( − 1 ) . {\displaystyle \prod _{s\ni e}1-x_{s}^{}\approx \prod _{s\ni e}\exp(-x_{s}^{})=\exp {\Big (}-\sum _{s\ni e}x_{s}^{}{\Big )}\approx \exp(-1).} So only a constant fraction of the elements will be covered in expectation. To make x ′ {\displaystyle x'} cover every element with high probability, the standard rounding scheme first scales up the rounding probabilities by an appropriate factor λ > 1 {\displaystyle \lambda >1} . Here is the standard rounding scheme: Fix a parameter λ ≥ 1 {\displaystyle \lambda \geq 1} . For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( λ x s ∗ , 1 ) {\displaystyle \min(\lambda x_{s}^{},1)} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . Scaling the probabilities up by λ {\displaystyle \lambda } increases the expected cost by λ {\displaystyle \lambda } , but makes coverage of all elements likely. The idea is to choose λ {\displaystyle \lambda } as small as possible so that all elements are provably covered with non-zero probability. Here is a detailed analysis. ==== Lemma (approximation guarantee for rounding scheme) ==== Fix λ = ln ⁡ ( 2 | U | ) {\displaystyle \lambda =\ln(2|{\mathcal {U}}|)} . With positive probability, the rounding scheme returns a set cover x ′ {\displaystyle x'} of cost at most 2 ln ⁡ ( 2 | U | ) c ⋅ x ∗ {\displaystyle 2\ln(2|{\mathcal {U}}|)c\cdot x^{}} (and thus of cost O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} times the cost of the optimal set cover). (Note: with care the O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} can be reduced to ln ⁡ ( | U | ) + O ( log ⁡ log ⁡ | U | ) {\displaystyle \ln(|{\mathcal {U}}|)+O(\log \log |{\mathcal {U}}|)} .) ==== Proof ==== The output x ′ {\displaystyle x'} of the random rounding scheme has the desired properties as long as none of the following "bad" events occur: the cost c ⋅ x ′ {\displaystyle c\cdot x'} of x ′ {\displaystyle x'} exceeds 2 λ c ⋅ x ∗ {\displaystyle 2\lambda c\cdot x^{}} , or for some element e {\displaystyle e} , x ′ {\displaystyle x'} fails to cover e {\displaystyle e} . The expectation of each x s ′ {\displaystyle x'_{s}} is at most λ x s ∗ {\displaystyle \lambda x_{s

Test data management

Test data management (TDM) is a process in software testing concerned with the creation, preparation, and control of data used for testing software systems. It involves supplying datasets required to execute test cases and verifying system behaviour under defined conditions. Test data management is an integral part of the software development lifecycle (SDLC) and is utilized in both manual and automated testing processes. It is applied in environments that use continuous integration and DevOps practices, where test execution requires consistent and repeatable data conditions. == Overview == Test data management includes the generation, selection, and preparation of data for testing purposes, as well as its distribution across test environments. It also involves controlling data versions and ensuring that datasets correspond to specific test scenarios. In many cases, production data is adapted for testing through techniques such as masking or subsetting to reduce size and remove sensitive content. Test data management ensures that test cases are executed with relevant, consistent, and readily available data. This reduces variability in test results and supports reproducibility across test cycles. == Importance == The role of test data management has expanded with the growth of complex, data-driven systems and regulatory requirements governing data usage. Testing often depends on data that reflects real-world conditions, but direct use of production data may introduce security and privacy risks. As a result, organizations apply methods such as data masking and anonymization to meet compliance requirements, including those set by the California Privacy Rights Act (CPRA) and Europe’s General Data Protection Regulation (GDPR). Inadequate control of test data can lead to incomplete test coverage, unreliable test results, or delays in testing processes due to unavailable or inconsistent datasets. == Techniques and tools == Test data management leverages various techniques for preparing and controlling data used in testing. These include the generation of synthetic data, the extraction of subsets from production datasets, and the modification of data to remove or obscure sensitive information. A key technical requirement in these processes is maintaining referential integrity, or ensuring that relationships between data entities remain consistent across different tables and systems after masking or subsetting. Data virtualization is also used to provide access to datasets without full replication. These methods may be implemented using software tools that automate data preparation, masking, and distribution.

Tabletopia

Tabletopia is an online portal for users to play and create virtual tabletop games. The platform is developed by Tabletopia Inc and initially was released as a web browser based service after a successful crowdfunding campaign in August 2015. In December 2016 Tabletopia was released on Steam, and later in 2018 became available in AppStore and Google Play. == Gameplay == Tabletopia is a sandbox system for running any game. That means no AI or rules enforcement. Participating players will have to know how to play the game. Nevertheless, the platform has some automated actions available, like card-shuffling and dealing, dice-rolling, magnetic placement of components in special zones, hand management, and some others. Tabletopia also features ready game setups for various player numbers to facilitate gameplay. It also has customisable camera controls which let players save camera positions and switch between them using hot keys. People can use the Game Designer mode to design and create their own board games using the component library. They can then monetise the games with a 70/30 split to the game designer. == Development == Tabletopia was created in early 2014, by Tim Bokarev and his partners Artem Zinoviev and Dmitry Sergeev. These co-founders already had experience in the video and board games industry. Their other projects include Promo Interactive, an internet advertising agency, Playtox, a mobile MMORPG, Igrology, a game studio, and Tesera.ru, the main Russian-speaking board gaming portal. By Spring 2014, Artem, Dmitry and Tim created Tabletopia Inc. USA and started development. Tabletopia is a multinational crew that includes professionals from USA, Ukraine, Australia, Ireland, and Germany. The Kickstarter campaign in August 2015 earned $133,721 by 2,545 backers. Tabletopia received Green Light on Steam in September 2015 and was released on Steam in March 2016. The platform remained in Early Access until December 2016, when it was officially released on Steam and on the web. In February 2018 it was released as a stand-alone app for iOS tablets, and in September 2018 for Android tablets.

AIX Toolbox for Linux Applications

The AIX Toolbox for Linux Applications is a collection of GNU tools for IBM AIX. These tools are available for installation using Red Hat's RPM format. == Licensing == Each of these packages includes its own licensing information and while IBM has made the code available to AIX users, the code is provided as is and has not been thoroughly tested. The Toolbox is meant to provide a core set of some of the most common development tools and libraries along with the more popular GNU packages.

Wave Financial

Wave is a Canadian company that provides financial services and software for small businesses. Wave is headquartered in the East Bayfront neighbourhood in Toronto, Canada. The company's first product was free online accounting software designed for businesses with 1–9 employees, followed by invoicing, personal finance and receipt-scanning software (OCR). In 2012, Wave began branching into financial services, initially with Payments by Wave (credit card processing) and Payroll by Wave, followed in February 2017 by Lending by Wave, which has since been discontinued. == History == CEO Kirk Simpson and CPO James Lochrie launched Wave Accounting Inc. in July 2009, Wave Accounting launched to the public on November 16, 2010. In June 2011, Series A funding led by OMERS Ventures was closed. In September 2011, FedDev Ontario invested one million dollars in funding. In October 2011, a $5-million investment led by U.S. venture capital firm Charles River Ventures was announced. In May 2012, Wave Accounting closed its series B financing round led by The Social+Capital Partnership, with follow-on participation from Charles River Ventures and OMERS Ventures. Wave acquired a company called Small Payroll in November 2011, which was later launched as a payroll product called Wave Payroll. In February 2012, Wave officially launched Wave Payroll to the public in Canada, followed by the American release in November of the same year. In August, 2012, the company announced the acquisition of Vuru.co, an online stock-tracking service. Terms of the deal were not disclosed. In December 2012, the company rebranded itself as Wave to emphasize its broadened spectrum of services. On March 14, 2019, the company acquired Every, a Toronto-based fintech company that provides business accounts and debit cards to small businesses. On June 11, 2019, the company announced it was being acquired by tax preparation company, H&R Block, for $537 million. On June 15, 2022, Wave announced that Kirk Simpson would be leaving and being replaced as CEO by Zahir Khoja. In May 2025, US customers of Wave were transitioned to a new Payroll processing system supported by CheckHQ. The new integration improved support for US employers by handling employer tax withholding and payments in all 50 US States. == Products == The company's initial product, Accounting by Wave, is a double entry accounting tool. Services include direct bank data imports, invoicing and expense tracking, customizable chart of accounts, and journal transactions. Accounting by Wave integrates with expense tracking software Shoeboxed and e-commerce website Etsy. The next product launched was Payroll by Wave, which was launched in 2012 after the acquisition of SmallPayroll.ca. Payroll by Wave is only available in the US and Canada. Invoicing by Wave is an offshoot of the company's earlier accounting tools. Additional products launched on or shortly after the company's rebrand in December 2012 include: a credit card processing tool, Payments by Wave, built initially on integration with Stripe credit card processing. However, Wave does not report merchant fees correctly for countries where Stripe charges a tax such as GST. In these cases, the merchant fees are reported without tax and do not match your Stripe account. a receipt scanning tool, Receipts by Wave. In 2017, Wave signed an agreement to provide its platform on RBC's online business banking site. The RBC-Wave service will be co-branded. == Taxes supported == The company's software supports tax-exclusive pricing, such as U.S. sales tax, where taxes are added on top of prices quoted. This has two effects: When scanning receipts users must manually add the tax, and input the amount. When making an invoice, users must put in a price before tax, and the system will add the tax on top. This makes Wave unable to handle taxes in countries like Australia where prices must be quoted inclusive of all taxes, such as GST. There is no way to set an invoice total and have Wave calculate the tax portion as a percentage. == Pricing and business model == As of June 10, 2024, Wave offers two tiers for its software: a free Starter plan with limitations on some features, and a paid Pro plan. In addition to its paid plan, revenue from the company comes from other paid financial services the company offers: Payments by Wave: Card processing which includes debit, credit and prepaid cards as well as ACH (bank payments) in the United States. Fees are a percentage of the transaction. Payroll by Wave: Monthly subscription fee plus usage fees. Wave previously included advertising on its pages as a source of revenue. Advertising was removed in January 2017. In 2017, Wave raised $24m (USD) in funding led by NAB Ventures. In 2019, H&R Block announced the acquisition of Wave in a cash deal worth $405 million USD.

Randonautica

Randonautica (a portmanteau of "random" + "nautica") is an app launched on February 22, 2020 founded by Auburn Salcedo and Joshua Lengfelder. It randomly generates coordinates that encourages the user to explore their local area and report what is found. According to its creators, the app is "an attractor of strange things," letting one choose specific coordinates based on a specific theme. It gained controversy after a report of two teenagers coincidentally finding a corpse while using the application. == Overview == The app, which creators claim to be inspired by chaos theory and Guy Debord's Theory of the Dérive, offers its users three types of coordinates to choose from: an attractor, a void, or an anomaly. The app has a cult following on YouTube and TikTok and there is a subreddit made by the creators for users of the app. == History == 29-year-old circus performer Joshua Lengfelder discovered a bot called Fatum Project in a fringe science chat group on Telegram in January 2019. According to The New York Times, "He absorbed the project’s theories about how random exploration could break people out of their predetermined realities, and how people could influence random outcomes with their minds." Lengfelder then created a Telegram bot using Fatum Project's code, generating coordinates. He then created the subreddit r/randonauts in March. In October, developer Simon Nishi McCorkindale made the bot's webpage. With the help of Auburn Salcedo, chief executive of a TV agency, both created Randonauts LLC. Salcedo became the chief operating officer while Lengfelder was the CEO. The app, called Randonautica, was launched on February 22, 2020. Later the same year the app and back-end got completely overhauled by a new team of developers and got a more visual and friendlier design and logo. In April 2022 Lengfelder exited Randonauts LLC and Auburn Salcedo became CEO. == Reception == The app has as many as 10.8 million users as of July 2020, gaining popularity amid the COVID-19 pandemic in the United States as restrictions have been lightened. Emma Chamberlain made a YouTube video about the app that helped increase its following. i-D reported that the hashtag #randonautica has gained 176.5 million views on TikTok, although it has not marketed itself yet. === Controversy === With the app's popularity, users started reporting coincidences which many find unsettling. The majority of reports were from TikTok and Reddit, as well as Telegram. The most notable controversy involved a group of people heading to a beach in Duwamish Head, Puget Sound, West Seattle per the app, where they found a bag with two dead bodies, a 27-year-old male and a 36-year-old female, as reported by the Seattle Police homicide detectives. In August 2020, police arrested and charged their landlord, Michael Lee Dudley, in connection with the murders. In March 2021, Dudley was denied bail while other people were under suspicion of aiding Dudley in the dismemberment and disposal of the bodies, but no one else had been charged. This has caused speculation that the app has an intended, puzzle-like theme. However, Lengfelder stated that it is "a shocking coincidence." Salcedo called the videos fake, and that "It’s so hard to manage, because people are really taking creative liberties after seeing how much traction the app is getting in that fear factor." In 2022, Michael Dudley was convicted of second degree murder for killing both victims, who were identified as Jessica Lewis and Austin Wenner. He was sentenced to 46 years in prison the following year. In their questions page, Randonautica's creators have said that if the app generates coordinates inside a private property, it is a violation of their terms and conditions to trespass. In addition, Randonautica has also received allegations that the app is used for human trafficking, which its creators have denied, saying that data collected by the app are anonymous. It also ensured that the app is not designed to violate religious customs, saying that "the app is simply a tool. Just as a knife can be used either to prepare dinner or to cut somebody."

Web application

A web application (or web app) is application software that is created with web technologies and runs via a web browser. Web applications emerged during the late 1990s and allowed for the server to dynamically build a response to the request, in contrast to static web pages. Web applications are commonly distributed via a web server. There are several different tier systems that web applications use to communicate between the web browsers, the client interface, and server data. Each system has its own uses as they function in different ways. However, there are many security risks that developers must be aware of during development; proper measures to protect user data are vital. Web applications are often constructed with the use of a web application framework. Single-page applications (SPAs) and progressive web apps (PWAs) are two architectural approaches to creating web applications that provide a user experience similar to native apps, including features such as smooth navigation, offline support, and faster interactions. Web applications are often fully hosted on remote cloud services, can require a constant connection to them, and can replace conventional desktop applications for operating systems such as Microsoft Windows, thus facilitating the operation of software as a service as it grants the developer the power to tightly control billing based on use of the remote services as well as vendor lock-in by hosting data remotely. Modern browsers such as Chrome offer sandboxing for every browser tab which improves security and restricts access to local resources. No software installation is required as the app runs within the browser which reduces the need for managing software installations. With the use of remote cloud services, customers do not need to manage servers as that can be left to the developer and the cloud service and can use the software with a relatively low power, low-resource PC such as a thin client. The source code of the application can stay the same across operating systems and devices of users with the use of responsive web design, since it only needs to be compatible with web browsers which adhere to web standards, making the code highly portable and saving on development time. Numerous JavaScript frameworks and CSS frameworks facilitate development. == History == The concept of a "web application" was first introduced in the Java language in the Servlet Specification version 2.2, which was released in 1999. At that time, both JavaScript and XML had already been developed, but the XMLHttpRequest object had only been recently introduced on Internet Explorer 5 as an ActiveX object. Beginning around the early 2000s, applications such as "Myspace (2003), Gmail (2004), Digg (2004), [and] Google Maps (2005)," started to make their client sides more and more interactive. A web page script is able to contact the server for storing/retrieving data without downloading an entire web page. The practice became known as Ajax in 2005. Eventually this was replaced by web APIs using JSON, accessed via JavaScript asynchronously on the client side. In earlier computing models like client-server, the processing load for the application was shared between code on the server and code installed on each client locally. In other words, an application had its own pre-compiled client program which served as its user interface and had to be separately installed on each user's personal computer. An upgrade to the server-side code of the application would typically also require an upgrade to the client-side code installed on each user workstation, adding to the support cost and decreasing productivity. Additionally, both the client and server components of the application were bound tightly to a particular computer architecture and operating system, which made porting them to other systems prohibitively expensive for all but the largest applications. Later, in 1995, Netscape introduced the client-side scripting language called JavaScript, which allowed programmers to add dynamic elements to the user interface that ran on the client side. Essentially, instead of sending data to the server in order to generate an entire web page, the embedded scripts of the downloaded page can perform various tasks such as input validation or showing/hiding parts of the page. "Progressive web apps", the term coined by designer Frances Berriman and Google Chrome engineer Alex Russell in 2015, refers to apps taking advantage of new features supported by modern browsers, which initially run inside a web browser tab but later can run completely offline and can be launched without entering the app URL in the browser. == Structure == Traditional PC applications are typically single-tiered, residing solely on the client machine. In contrast, web applications inherently facilitate a multi-tiered architecture. Though many variations are possible, the most common structure is the three-tiered application. In its most common form, the three tiers are called presentation, application and storage. The first tier, presentation, refers to a web browser itself. The second tier refers to any engine using dynamic web content technology (such as ASP, CGI, ColdFusion, Dart, JSP/Java, Node.js, PHP, Python or Ruby on Rails). The third tier refers to a database that stores data and determines the structure of a user interface. Essentially, when using the three-tiered system, the web browser sends requests to the engine, which then services them by making queries and updates against the database and generates a user interface. The 3-tier solution may fall short when dealing with more complex applications, and may need to be replaced with the n-tiered approach; the greatest benefit of which is how business logic (which resides on the application tier) is broken down into a more fine-grained model. Another benefit would be to add an integration tier, which separates the data tier and provides an easy-to-use interface to access the data. For example, the client data would be accessed by calling a "list_clients()" function instead of making an SQL query directly against the client table on the database. This allows the underlying database to be replaced without making any change to the other tiers. There are some who view a web application as a two-tier architecture. This can be a "smart" client that performs all the work and queries a "dumb" server, or a "dumb" client that relies on a "smart" server. The client would handle the presentation tier, the server would have the database (storage tier), and the business logic (application tier) would be on one of them or on both. While this increases the scalability of the applications and separates the display and the database, it still does not allow for true specialization of layers, so most applications will outgrow this model. == Security == Security breaches on these kinds of applications are a major concern because it can involve both enterprise information and private customer data. Protecting these assets is an important part of any web application, and there are some key operational areas that must be included in the development process. This includes processes for authentication, authorization, asset handling, input, and logging and auditing. Building security into the applications from the beginning is sometimes more effective and less disruptive in the long run. == Development == Writing web applications is simplified with the use of web application frameworks. These frameworks facilitate rapid application development by allowing a development team to focus on the parts of their application which are unique to their goals without having to resolve common development issues such as user management. In addition, there is potential for the development of applications on Internet operating systems, although currently there are not many viable platforms that fit this model.