progres_tme_3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Progres: TME3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fabien Mathieu - fabien.mathieu@normalesup.org\n",
    "\n",
    "Sébastien Tixeuil - Sebastien.Tixeuil@lip6.fr\n",
    "\n",
    "**Note :**\n",
    "\n",
    "- The starred exercises (indicated by *) must be done only if all other exercises have been done. You do not have to do them to get a score of 20/20.\n",
    "\n",
    "- stackoverflow is your friend... But if you use something you find on the Internet, you have to cite your source AND add explanations. If you copy/paste something without explanation, you won't get the maximum score even if it works!\n",
    "\n",
    "- The examples given are just examples, you are not obliged to display exactly the same thing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TME3 objective"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The goal of TME3 is to simulate a distributed hash table based on Chord. *Simulating* means that we won't go to the *prototype*, but only look at the interesting mechanisms in the context of a DHT: building routing tables, insertions, etc...\n",
    "\n",
    "Concretely, we'll ignore all the problems related to the network implementation itself (launching independent clients in VMs, managing network connections, ...) and run everything centrally assuming that the primitives exist, and trying not to call primitives as if they came from peers.\n",
    "\n",
    "**Note:** Normally, after this TME, you will have all the basic notions to make a more realistic implementation of Chord, typically at the mini-project level."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will reproduce the table example given in the course."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cell below is just to display the Chord ring. No need to evaluate it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T07:25:02.877610Z",
     "start_time": "2022-11-25T07:24:59.750329Z"
    },
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%tikz --size 500,500\n",
    "\\draw (0,0) circle (2) ;\n",
    "\\foreach \\n/\\a in {1/84,8/45,14/11,21/331,32/270,38/236,42/214,48/180,51/163,56/135}\n",
    "{\\node[blue] (\\n) at (\\a:2) {$\\bullet$} ;\n",
    "\\node (p\\n) at (\\a:2.4) {$p_{\\n}$} ;}\n",
    "\\draw[->,>=latex] (8) edge (14) edge (21) edge (32) edge (42);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity, we will identify a peer and its key. In particular, if you know the key of a peer, you can contact him. In real life, of course, you also need a real IP address or something like that. For example, $p_{38}$ is represented by something like (name: mymachine, ip: 129.199.129.1, hash: 38, ...). For the TME, we'll settle for 38."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 1: centralized building"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To start with, we assume a complete knowledge of the network and build the different routing tables.\n",
    "\n",
    "We assume that we have an already populated and functional DHT. The size of the key space is 64 and we have access to the peer list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T07:04:07.817409Z",
     "start_time": "2022-11-25T07:04:07.801166Z"
    }
   },
   "outputs": [],
   "source": [
    "Nmax = 64\n",
    "peers = [1, 8, 14, 21, 32, 38, 42, 48, 51, 56]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a successor function that returns the successor of a key, and a predecessor function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Be careful, we are not trying to do Chord yet, it is just about giving the answer from the complete knowledge of the system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Typically, with these functions, you should be able to write:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T07:04:09.754624Z",
     "start_time": "2022-11-25T07:04:09.440941Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[32, 48, 1]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[successor(k, peers) for k in [30, 42, 60]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T06:34:35.012537Z",
     "start_time": "2022-11-25T06:34:34.999086Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[32, 56]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[predecessor(k, peers) for k in [37, 1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a function that returns a dictionary associating to each peer its own key, its successor, its predecessor and its finger table."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, you can use the complete knowledge of the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T07:04:30.469004Z",
     "start_time": "2022-11-25T07:04:30.441246Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: {'key': 1, 'next': 8, 'prev': 56, 'finger': [8, 14, 21, 38]},\n",
       " 8: {'key': 8, 'next': 14, 'prev': 1, 'finger': [14, 21, 32, 42]},\n",
       " 14: {'key': 14, 'next': 21, 'prev': 8, 'finger': [21, 32, 48]},\n",
       " 21: {'key': 21, 'next': 32, 'prev': 14, 'finger': [32, 38, 56]},\n",
       " 32: {'key': 32, 'next': 38, 'prev': 21, 'finger': [38, 42, 51, 1]},\n",
       " 38: {'key': 38, 'next': 42, 'prev': 32, 'finger': [42, 48, 56, 8]},\n",
       " 42: {'key': 42, 'next': 48, 'prev': 38, 'finger': [48, 51, 1, 14]},\n",
       " 48: {'key': 48, 'next': 51, 'prev': 42, 'finger': [51, 56, 1, 21]},\n",
       " 51: {'key': 51, 'next': 56, 'prev': 48, 'finger': [56, 1, 8, 21]},\n",
       " 56: {'key': 56, 'next': 1, 'prev': 51, 'finger': [1, 14, 32]}}"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dht = make_dht(peers)\n",
    "dht"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2: using Chord "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should now have correctly configured Chord routing tables. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test whether a peer $i$ is in charge of a key $k$. This function must be executed from the peer's point of view, i.e. using only the data owned by $i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T06:37:37.504854Z",
     "start_time": "2022-11-25T06:37:37.490794Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = 1; k = 56\n",
    "isincharge(dht[i], k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T06:37:38.228614Z",
     "start_time": "2022-11-25T06:37:38.200586Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 55\n",
    "isincharge(dht[i], k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T06:39:22.466069Z",
     "start_time": "2022-11-25T06:39:22.447747Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[32, 33, 34, 35, 36, 37]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = 38\n",
    "[k for k in range(Nmax) if isincharge(dht[i], k)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a key search function, which will return the route to reach the peer responsible for a key."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T00:23:20.967276Z",
     "start_time": "2022-11-25T00:23:20.942808Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8, 42, 51, 56]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lookup(8, 54, dht)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T00:23:21.532153Z",
     "start_time": "2022-11-25T00:23:21.509226Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[42, 14, 21]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lookup(42, 14, dht)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T00:23:22.020542Z",
     "start_time": "2022-11-25T00:23:22.008362Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[42, 14, 21, 32]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lookup(42, 21, dht)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 3: decentralized building "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting with a full table it is easy. Let's start from the beginning, with a single even number, 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T07:04:44.398067Z",
     "start_time": "2022-11-25T07:04:44.380920Z"
    }
   },
   "outputs": [],
   "source": [
    "dht2 = {1: {'key': 1, 'next': 1, 'prev': 1, 'finger': []}}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The routing is very minimalist for the moment..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T06:42:12.725539Z",
     "start_time": "2022-11-25T06:42:12.703101Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lookup(1,42, dht2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a peer $p$ and a set of peers, construct a finger table for $p$. Note: a peer should never return to its own routing table, and the table must not contain duplicates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T06:42:51.938338Z",
     "start_time": "2022-11-25T06:42:51.924820Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[22, 32, 60]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "build_finger(15, [1, 3, 60, 32, 7, 15, 45, 22, 60])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-25T06:42:52.864136Z",
     "start_time": "2022-11-25T06:42:52.844783Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[56, 1]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "build_finger(42, [1, 56, 42])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a function to insert a peer as seen in course, using 1 as the insertion point.\n",
    "\n",
    "Insert peers 8, 14, ... in the order you want\n",
    "\n",
    "- Do you have a working table?\n",
    "- How complete is it? (compare with Exercise 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Réponse :**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3.3*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Propose solutions to have more complete tables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 4: to go further*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4.1*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Manage the clean departure of a peer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4.2*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use a larger key space (e.g. 32 bits), and insert more peers (10000)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4.3*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate 100,000 keys and study their distribution over the 10,000 peers:\n",
    "- How many keys are managed at most by a peer?\n",
    "- Draw a curve that gives the number of peers that have $x$ keys (as a function of $x$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4.4*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute 100 *lookup* from random keys and peers:\n",
    "- What is the maximum lookup length?\n",
    "- Draw a curve that gives the number of lookups of length $x$ (as a function of $x$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  }
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