Matthew Hutchinson

What is ‘Computational Complexity’ ?

Basically a theory describing the scalability of algorithms. “As the size of the input to an algorithm increases, how do the running time and memory requirements of the algorithm change?” Wikipedia has a more complete description. Complexity can be considered in terms of;

• Time Complexity – the number of steps that it takes to solve an instance of the problem as a function of the size of the input, using the most efficient algorithm.
• Space Complexity – the amount of space, or memory required by the algorithm.

If you consider an array with n elements, and in solving a problem on this array, it takes n times n (or n²) steps. You could say the algorithm used had a complexity of n². Now with different programming languages there may be additional steps in the algorithm necessary to solve the problem. To describe a general level of complexity across any language, the Big Oh Notation is used. So the time-complexity for this algorithm would be Θ(n²)

‘Θ’ basically indicates that we are ignoring any language dependent factors, allowing complexity to be expressed purely in terms of the size of the input.

An Example

if you take a simple problem like, finding the ‘mode’ average on an array. I.e. the most frequently occurring element in a sequence (lets say of numbers) – You could do this an number of ways. Here is a brute force attempt (in Ruby).

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def calculate_mode(nums)
  hi_count = 0
  mode = nums[0]
  nums.each do | search_for |
    count = 0
    nums.each do |num|
      if search_for == num
        count += 1
      end
    end
    if count > hi_count
      hi_count = count
      mode = search_for
    end
  end
end

It should be obvious that this algorithm has a complexity of Θ(n²) – since every element of the array must be searched by each element to find the highest count value (and hence the mode).

Could it be done any faster? If the array of elements was sorted (ordered numerically) – the mode could be found by finding the longest continuing sequence in the array, that should only take n iterations. Employing a quick sort algorithm first; which can sort (on average) with Θ(n log n)

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def quicksort(a)
  return a if a.size <= 1
  pivot = a[0]
  quicksort(a.select {|i| i < pivot }) +
      a.select {|i| i == pivot } + 
      quicksort(a.select {|i| i > pivot })  
end

def calculate_mode_fast(nums, time_start)
  # sort array first
  sorted_nums = quicksort(nums)

  hi_count = 0
  mode = nums[0]  
  count = 1
  idx = 1

  sorted_nums.each do | search_for |
   if search_for == sorted_nums[idx]
     count += 1
     if count > hi_count
       hi_count = count
       mode = search_for
     end
   else
     count = 1
   end
   idx += 1 if idx < sorted_nums.length
  end
end

So we could say that this approach has (on average) a complexity of Θ(n+(n log n)) which is significantly less that Θ(n²)

I’ve posted this code listing which implements both algorithms running to compute the modal average on identical arrays of random integers. You can vary n (the number of elements) to see how each method performs. From the results (below) its clear that the 2nd algorithm is more time-efficient in this case.

calculate_mode
====================
mode => 3 (it occurs 44 times)
array length was 1000
num loops was 1000000
completed in 0.71737

calculate_mode_fast
=========================
mode => 3 (it occurs 44 times)
array length was 1000
num loops was 1040
completed in 0.011247

You might have noticed a minor style change in the most recent blog entries. I’ve decided (from now on) to use a light-box for showing off any embedded videos and (biggish) images on the page. It keeps the layout tidy and allows you to focus on the video you’re watching or image your viewing, without distraction. So I can do things like this for images;

And even stuff like this, for videos

All of this is made possible using Control.Modal, a light weight, unobtrusive JavaScript library for creating modal windows and lightboxes using content that is already on the page. So with javascript turned off, everything still works, with the links navigating to anchor tags in the page.

At the moment I am applying display:none; on the modal content to avoid a visible onLoad jump effect as the content gets hidden by Control.Modal javascript. I’ll be changing this (since doing this hides the content when javascript is off, and CSS is on) – There’s also a small bug with the tv-icon link style on IE6.

In Mephisto, I was able to create my own custom ‘Modal Macro’ filter, so I can easily apply the effect to any content in my articles. Here is the code for doing just that. Save this as modal_macro.rb in the lib/ folder for any new or existing vendor/plugin. As usual, any comments, questions or suggestions are appreciated.

Here are some links that may be of use to anyone getting started with REST Resources in Rails.

• Dont say CRUD say FUCD – (DHH introduction with slides and link to walkthrough)
• Documentation on the orginal RESTFul plugin
• NESTED CRUD Resources in Rails
• REST and Rails no reason to be scared
• Almost ALL Rails Conf Euro Videos – watch the DHH one on Vendoritis
• Peepcode tutorial 9$ screencast – with free cheatsheet
• REST on Rails
• Simply RESTful Support – And How to Use It
• Rails nested resource scaffold
• World of Resources, Loud Thinking

Some years ago I made use of a Windows based (and free) packet analsyer tool Packetyzer, from Network Chemistry) It did the job and proved to be invaluable for testing and building different packet headers – for projects just like this – but as a fan of Ruby, I had to see if this could be done in the language of my choice.

Just a few months ago I began doing a little research into GPRS packets for a potential ‘location-based’ mobile web service. To do this I was hoping to use Ruby and through pCap I was able to.

To start monitoring packets, you’ll first have to install libpcap – a low level packet capture library (authored in C) – from LBNL’s Network Research Group You can follow this short tutorial to do this. The libpcap library grabs packets from any network adaptor on your system, giving you the raw data to work with. Doing this is immensely powerful, you could write listeners to monitor anything from email traffic to instant message conversations (provided the traffic isn’t encrypted of course).

Next, to allow us to write Ruby code to interface with this library, you’ll need to install pcaplet – This Ruby binding library makes writing capture programs easy. Its as simple as using require ‘pcaplet’ at the head of your Ruby code and your off.

I was able to use these libraries to examine TCP/IP packets from my mobile device (sent via GPRS over TCP/IP) to my server. The following Ruby script extracted the information I was interested in (data addressed to HTTP) using a regular expression;

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#!/usr/bin/env ruby

require 'pcaplet'

# create a sniffer that grabs the first 1500 bytes of each packet
$network = Pcaplet.new('-s 1500')

# create a filter that uses our query string and the sniffer we just made
$filter = Pcap::Filter.new('tcp and dst port 80', $network.capture)
$network.add_filter($filter)

# the packet sniffer loop
for p in $network
  # if the packet matches the filter and the regexp...
  if $filter =~ p and p.tcp_data =~ /GET(.*)HTTP.*/
    # print all packet data for each packet that matches
     puts p.tcp_data
  end
end

Then save this and run the script with something like;

ruby packet_filter_regex.rb 
# you may need to run this as root if you have permission problems

The add_filter function, with ‘tcp and dst port 80’ – means all tcp traffic directed at port 80 on the adapter, this resource details all the tcpdump syntax for different filter designs. This code will be a useful tool for me in another project -looking at streaming video and audio.

Another article at Linux.Ars roughly describes what is behind this and shows some more example Ruby scripts for packet monitoring (including an aim chat sniffer). There are also a few more example filters on the pcaplet site.

Apr-07 UPDATE – Sylvain Sarmejeanne has just released Scruby a Ruby application that works on UNIX providing a shell where you can perform packet creation, sending and sniffing functions in a Ruby-esque fashion. It requires libpcap and uses PCapRub (a mininal PCAP wrapper) rather than using PCAP directly. The package is well documented and has an irb-like interface, accepting command line input for debugging.

For some time now I have been trying out ActiveCollab, a free project management tool, to see if it could be a decent competitor to Basecamp

As far as I know, ActiveCollab started out as a free alternative to (and almost straight copy of) Basecamp – It is open source, written in PHP, and version 0.7 was released just a few weeks ago. After installing and setting up an example project I really needed to see how the thing would run with some real data, y’know some real life stuff.

After playing around with the (very useful) Basecamp API I had created a little Ruby class that allowed me to import projects, users, messages, comments and categories into ActiveCollab from Basecamp.

Run from the command line, the class outputs SQL (to the screen or a file) – which you can run against your ActiveCollab database after a default install. Read on if you’re interested in how it works.

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