Heapsort

With its time complexity of O(n log(n)) heapsort is optimal. It utilizes a special data structure called heap. This data structure is explained in the following.

Basics

Definition: Let T = (V, E) an almost complete binary tree with a vertex labelling a : V  M that assigns to each vertex u a label a(u) from an ordered set (M, ).

A vertex u  V has the heap property if it has no direct descendant with a greater label, i.e.

 v  V  :  (u, v)  E      a(u)  a(v)

T is a heap if all vertices have the heap property, i.e.

 (u, v)  E  :  a(u)  a(v)

We call T a semi-heap if all vertices except possibly the root r have the heap property, i.e.

 (u, v)  E,  ur  :  a(u)  a(v)

Example:

Figure 1:  Heap with n = 10 vertices

Observe that each leaf automatically has the heap property regardless of its label, since it has no descendants. >>>>

XenSource CTO Simon Crosby Talks Up Xen Virtualization

Virtualization — the use of multiple instances of operating systems, applications, or other software running on single hardware devices — comes in many different forms and flavors, but among the most often mentioned of late is XenSource and its open source Xen virtualization technology.

While still not on the scale of virtualization giant VMware in terms of either features or popularity, Xen has been highly anticipated and is now the subject of a significant debate over its readiness for business production environments.

Xen also recently announced an interoperability arrangement with Microsoft (Nasdaq: MSFT) , prompting harsh criticism from some, but also paving the way for further interoperability between Linux and Windows when it comes to virtualization in the datacenter.

LinuxInsider caught up with XenSource Chief Technology Officer Simon Crosby recently to discuss Xen’s Linux and Windows interoperability, and to find out what we might expect to see next from Xen. >>>>

Simplify data extraction using Linux text utilities

Much of Linux® system administration involves tediously combing through plain-text configuration files. Fortunately, Linux has a rich array of UNIX®-derived data extraction utilities, including head, tail, grep, egrep, fgrep, cut, paste, join, awk, and more. This article uses real-world examples that show how these simple command-line programs can make you a better sysadmin. This article looks at each data extraction utility and its options, applies them to typical files that are used in day-to-day work, and looks at how and why each tool is useful for pulling data from these files.

“); } } } //–> The Linux operating system is loaded with files: configuration files, text files, documentation files, log files, user files, and the list goes on and on. Quite often, those files contain information you need to access in order to find important data. Although you can easily dump the contents of most files to the screen with standard utilities such as cat, more, and others, there are utilities better suited for filtering and parsing out only those values that are relevant to you.

As you read this article, you can open your shell and try the examples of each utility. >>>>

The Linux kernel map -2.6.18

Here’s a easy to follow flowchart for all those who say linux is complicated.

Real to plug Windows media support into Linux

The media delivery software company and Novell made the announcement at the LinuxWorld Conference and Expo here. Novell said it will include the tool in its Suse Linux Enterprise Desktop 10 in the fourth quarter.

Currently, Linux users can play Windows Media Video (WMV) and Windows Media Audio (WMA) content if they install closed-source modules, said Jeff Duchmann, general manager of client and digital rights management technologies at RealNetworks. That will change as the result of a licensing deal RealNetworks has signed with Microsoft and its settlement of an antitrust suit against the software giant. It will release open-source code to play the files as part of the Helix Community project it launched to bring RealNetworks technology to Linux. >>>>

LinuxWorld: Novell touts SUSE Linux 10 downloads, customer wins

August 15, 2006 (Computerworld) — SAN FRANCISCO — At LinuxWorld today, Novell Inc. cited evidence of growing customer interest in its recently-released SUSE Enterprise Linux 10.

Waltham, Mass.-based Novell said it has received a combined 324,000 download requests for its SUSE Linux Enterprise Desktop and Server editions since their release one month ago — with slightly more downloads of the desktop edition, nicknamed SLED 10.

John Dragoon, Novell’s chief marketing officer, said the company hopes to convince up to 45 companies and organizations worldwide — including 15 in North America — to pilot the SLED 10 desktop in the next 12 months. “Our job is to convert mindshare into market share,” he said >>>>

CFQ to become the default I/O scheduler in 2.6.18

Judging by this commit, CFQ (Complete Fair Queuing) I/O scheduler will become the default one in the upcoming 2.6.18 kernel. For a long time, anticipatory scheduler has been the default, although even back in late 2004 there was some thinking about replacing it with CFQ. And it seems the time has finally come. CFQ scheduler has been gaining adoption since then, to the point that it’s the default I/O scheduler for RHEL 4, Suse, and other distros.

One of the coolest things about CFQ is that it features I/O priorities (since 2.6.13). That means you can set the I/O priority of a process so you can avoid that a process that does too much I/O (daily updatedb) starves the rest of the system, or give extra priority to a process that shouldn’t be starved by other processes, by using the ionice tool included in schedutils (since version 1.5.0).

If you find any problems with the new default scheduler, you can still continue using the AS scheduler, by switching to it at runtime (echo anticipatory > /sys/block/<disk>/queue/scheduler) or by using the elevator=as boot option.

Key Linux programmer moves to Google

Australian-born Andrew Morton, a key deputy to Linux leader Linus Torvalds, has taken a job at search engine powerhouse Google, a major user of Linux and other open-source software.

“For what it’s worth, I recently took a position with Google,” Morton said in a posting last week to the Linux kernel mailing list. Morton is responsible for maintaining the current 2.6 version of the Linux kernel, vetting new patches and working closely with Torvalds. Morton and Torvalds are paid by a consortium, Open Source Development Labs, but Morton actually worked at a company called Digeo Interactive. Now he’s moving offices to Google. >>>>

Glade 3 sees the light of day

The GUI designer tool that has been building your GTK+ applications for years is back with a completely new generation of homegrown free software. Supporting all the widgets in the gtk+ 2.8 familly, gnomeui widgets, the gnome canvas widget, and a whole new feature set; this new tool is sure to raise a few eyebrows.

Glade 3 has been a lingering myth for several years now. Originally thought up and designed by Chema Celorio, Damon Chaplin (author of the original Glade tool) and others who were around back in 2001 before GTK+ 2.0 was ever released; Glade was worked on vigorously by Chema, Carlos Perello Marin and others. Chema was an outstanding contributor to GNOME in many ways and was unfortunately taken from us in a skydiving accident in november 2003, this one goes out to you Chema! >>>>

Intel moving it’s chip designes to Linux on Laptop

Linux is widely used in electronic design automation (EDA) and computer-aided design (CAD), especially in chip and circuit design. Software from Synopsys Inc., Mentor Graphics Corp. and market leader Cadence Design Systems Inc. mostly run on the open-source operating system.

Intel served as the primary beta tester for the SUSE-equipped notebooks and is expected to eventually buy “thousands” of the laptops, according to Bill Iori, worldwide manager for ThinkPads at Lenovo.

PC makers have long been reluctant to preinstall Linux on their computers on a large scale because of concerns about offending Microsoft Corp. and uncertainty over which flavor of Linux to install or whether the market size justifies the cost.  >>>>