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closest-pair

A framework for Apache Mesos that given a file with a list of 2D points, calculates the closest distance between any two points in that set. Implements a divide-and-conquer algorithm which determines the result in O(nlogn) time instead of brute-force O(n^2).

Based on Rendler implementation.

Closest-Pair consists of two main components:

• ClosestPairExecutor extends mesos.Executor
• ClosestPairScheduler extends mesos.Scheduler

Quick Start with Vagrant

Requirements

• VirtualBox 4.1.18+
• Vagrant 1.3+
• git (command line tool)

Start the mesos-demo VM

$ wget http://downloads.mesosphere.io/demo/mesos.box -O /tmp/mesos.box
$ vagrant box add --name mesos-demo /tmp/mesos.box
$ git clone https://github.com/chenlily/closest-pair
$ vagrant up

Execution:

$ vagrant ssh
vagrant@mesos:~ $ cd hostfiles

# Update install dependencies
vagrant@mesos:cpp $ sudo apt-get update
vagrant@mesos:cpp $ sudo apt-get install libcurl4-openssl-dev libboost-regex1.55-dev \
          libprotobuf-dev libgoogle-glog-dev protobuf-compiler

# Build
vagrant@mesos:cpp $ make all

# Start the scheduler with the test file and the mesos master ip
vagrant@mesos:cpp $ ./closest-pair-scheduler testfile 127.0.1.1:5050
# <Ctrl+C> to stop...

Shutting down the mesos-demo VM

# Exit out of the VM
vagrant@mesos:hostfiles $ exit
# Stop the VM
$ vagrant halt
# To delete all traces of the vagrant machine
$ vagrant destroy

Test File Format

Points can be either integers or floating point

x1 y1
x2 y2
x3 y3 

Closest-Pair Architecture

Closest-Pair Scheduler

Data Structures

A point is represented by a struct x and y coordinates.

struct Point(
  double x,y; 
)

A split on an array into its left and right components is represented by a SplitInfo. It contains the left and right indices of its subarray, a parent ID, the minimum distances on its left and right halves, and also whether the split is a left or right child to its parent. If the split is the original/root array, the direction is set as NONE.

struct SplitInfo (
  int left, right parent; 
  double lMinDist, rMinDist; 

  // enum Direction {LEFT, RIGHT, NONE}; 
  Direction dir;   
)

• pointvector vector of Points containing the original array of Points
• splitQueue list of vectors to be split in half
• parentMap maps parentIDs to their splitInfo, also acts as a list of splitInfo whose minDistances still need to be calculated

Scheduler Behavior

The scheduler accepts a text file as command-line parameter to create a vector of points to calculate the minimum distance.

• Reads in the file and initializes a point vector
• Split each vector into two halves until it is 2 or fewer elements. On each split, create a SplitInfo object representing the split and insert it into the parentMap
• Until parentMap is empty, launch a combiner task to calculate the minDistance on splitInfo objects that minimum distances calculated on the left and right sides. Update splitInfo's parent through parentMap.
• Print the final minDistance through stdout

Combiner Executor

• Interprets incoming tasks' task.data field as an array of points, the subarray's parentID, minDistance on its left and right halves, and also whether the subarray is a left or right child to its parent
• Calculates the minDistance in that subarray of points
• Returns the subarray's minDistance, parentID, and relation to its parent to the scheduler in the data field of a TaskStatus