Probabilistic Pathfinding Simulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation to test cost functions for probabilistic path finding\n",
    "\n",
    "This notebook is a repsonse to https://github.com/ElementsProject/lightning/pull/4771 where Rusty Russel, Christian Decker and I discuss which cost function should be used in Sijkstra computations to test single paths if one wants to incorporate the results from proababilistic path finding research (c.f: https://arxiv.org/abs/2103.08576 )\n",
    "\n",
    "## Funding\n",
    "This work is funded by NTNU, Bitmex, and independent people tipping me via https://donate.ln.rene-pickhardt.de and via https://patreon.com/renepickhardt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "from math import log2\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A few helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def import_channels(filename):\n",
    "    f= open(filename,\"r\")\n",
    "    channels = json.load(f)[\"channels\"]\n",
    "    return channels\n",
    "\n",
    "def next_hop(path):\n",
    "    for i in range(1,len(path)):\n",
    "        src = path[i-1]\n",
    "        dest = path[i]\n",
    "        yield (src,dest)\n",
    "\n",
    "def arithmetic_mean(features):\n",
    "    return np.mean(features)\n",
    "\n",
    "def harmonic_mean(features):\n",
    "    return len(features)/sum(1.0/(f+1) for f in features)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define cost functions for single features that are potentially used in c-lighting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fee_function(amt,channel):\n",
    "    return channel[\"base_fee_millisatoshi\"]+amt*channel[\"fee_per_millionth\"]/1000000\n",
    "    \n",
    "def risk_factor_cltv(riskfactor,channel):\n",
    "    cltv_delay = channel[\"delay\"]\n",
    "    BLOCKS_PER_YEAR = 144*365\n",
    "    return riskfactor / 100.0 / BLOCKS_PER_YEAR * cltv_delay\n",
    "    \n",
    "def neg_log_probabilities(amt, channel):\n",
    "    cap = channel[\"satoshis\"]*1000\n",
    "    return -log2((cap+1-amt)/(cap+1))\n",
    "    \n",
    "def linearized_success_probabilities(amt,channel):\n",
    "    cap = channel[\"satoshis\"]*1000\n",
    "    return amt/(cap+1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Actual cost functions with combination of features "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_features(amt, channel, risk_factor=0):\n",
    "    features = {\n",
    "        \"fees\":fee_function(amt,channel),\n",
    "        \"neg_log_prob\":neg_log_probabilities(amt, channel)}\n",
    "    if risk_factor>0:\n",
    "        features[\"risk_factor\"]= risk_factor_cltv(risk_factor,channel)\n",
    "    return features\n",
    "    \n",
    "    \n",
    "def harmonic_probabilistic_cost(amt,channel,risk_factor=0):\n",
    "    features = build_features(amt,channel,risk_factor)\n",
    "    return harmonic_mean(features.values())\n",
    "\n",
    "def arithmetic_probabilistic_cost(amt,channel,risk_factor=0):\n",
    "    features = build_features(amt,channel,risk_factor)\n",
    "    return arithmetic_mean(list(features.values()))\n",
    "\n",
    "def rusty_proposed_cost(amt,channel,risk_factor=0):\n",
    "    f = fee_function(amt,channel)\n",
    "    p = linearized_success_probabilities(amt,channel)\n",
    "    r = risk_factor_cltv(risk_factor,channel)\n",
    "    return f*(1+p)+r\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import data from lightning-cli listchannels > channels20210918.json"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'active': True,\n",
       " 'amount_msat': '20000000msat',\n",
       " 'base_fee_millisatoshi': 0,\n",
       " 'channel_flags': 0,\n",
       " 'delay': 144,\n",
       " 'destination': '03fab7f8655169ea77d9691d4bd359e97782cb6177a6f76383994ed9c262af97a5',\n",
       " 'features': '',\n",
       " 'fee_per_millionth': 1,\n",
       " 'htlc_maximum_msat': '20000000msat',\n",
       " 'htlc_minimum_msat': '1000msat',\n",
       " 'last_update': 1631699351,\n",
       " 'message_flags': 1,\n",
       " 'public': True,\n",
       " 'satoshis': 20000,\n",
       " 'short_channel_id': '513909x1248x0',\n",
       " 'source': '02ad6fb8d693dc1e4569bcedefadf5f72a931ae027dc0f0c544b34c1c6f3b9a02b'}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "channels = import_channels(\"channels20210918.json\")\n",
    "channels[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa2578eda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa257dc080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa257c30b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa2584a4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa259642b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "values = list(range(1,20))\n",
    "\n",
    "plt.title(\"harmonic mean with cltv on 20k sats channel\")\n",
    "plt.plot(values,[harmonic_probabilistic_cost(amt*1000000,channels[0],1) for amt in values])\n",
    "plt.grid()\n",
    "plt.xlabel(\"amount sent in kilo Sats\")\n",
    "plt.ylabel(\"cost\")\n",
    "plt.show()\n",
    "plt.title(\"harmonic mean without cltv on 20k sats channel\")\n",
    "plt.plot(values,[harmonic_probabilistic_cost(amt*1000000,channels[0]) for amt in values])\n",
    "plt.grid()\n",
    "plt.xlabel(\"amount sent in kilo Sats\")\n",
    "plt.ylabel(\"cost\")\n",
    "plt.show()\n",
    "plt.title(\"arithmetic mean with cltv on 20k sats channel\")\n",
    "plt.plot(values,[arithmetic_probabilistic_cost(amt*1000000,channels[0],1) for amt in values])\n",
    "plt.grid()\n",
    "plt.xlabel(\"amount sent in kilo Sats\")\n",
    "plt.ylabel(\"cost\")\n",
    "plt.show()\n",
    "plt.title(\"arithmetic mean without cltv on 20k sats channel\")\n",
    "plt.plot(values,[arithmetic_probabilistic_cost(amt*1000000,channels[0]) for amt in values])\n",
    "plt.grid()\n",
    "plt.xlabel(\"amount sent in kilo Sats\")\n",
    "plt.ylabel(\"cost\")\n",
    "plt.show()\n",
    "plt.title(\"Rusty Proposed cost on 20k sats channel\")\n",
    "plt.plot(values,[rusty_proposed_cost(amt*1000000,channels[0]) for amt in values])\n",
    "plt.grid()\n",
    "plt.xlabel(\"amount sent in kilo Sats\")\n",
    "plt.ylabel(\"cost\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "   ## Create a graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_known_balance_graph(channels):\n",
    "    D = nx.DiGraph()\n",
    "    for chan in channels:\n",
    "        D.add_edge(chan[\"source\"],chan[\"destination\"],channel=chan)\n",
    "    for s,d in D.edges():\n",
    "        cap = D[s][d][\"channel\"][\"satoshis\"]\n",
    "        if s in D[d]:\n",
    "            if s<d:\n",
    "                D[s][d][\"balance\"]=random.randint(0,cap)\n",
    "                D[d][s][\"balance\"]=cap - D[s][d][\"balance\"]\n",
    "        else:\n",
    "            D[s][d][\"balance\"]=random.randint(0,cap)\n",
    "    return D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = make_known_balance_graph(channels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa274bf7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#check visualy that it is uniformly distributed\n",
    "plt.hist([D[s][d][\"balance\"]/D[s][d][\"channel\"][\"satoshis\"] for s,d in D.edges()])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prepare_experiment(D,cost_function,amt,risk_factor = 0):\n",
    "    res = nx.DiGraph()\n",
    "    for s,d in D.edges():\n",
    "        if D[s][d][\"channel\"][\"satoshis\"]*1000 < amt:\n",
    "            continue\n",
    "        res.add_edge(s,d,weight=cost_function(amt, D[s][d][\"channel\"],risk_factor))\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "bos_nodes = [x[\"public_key\"] for x in json.load(open(\"bos.json\",\"r\"))[\"scores\"]]\n",
    "LN_RENE_PICKHARDT=\"03efccf2c383d7bf340da9a3f02e2c23104a0e4fe8ac1a880c8e2dc92fbdacd9df\"\n",
    "amt_sats = 100000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "harmonic_with_cltv = prepare_experiment(D,harmonic_probabilistic_cost,1000*amt_sats,1)\n",
    "harmonic_no_cltv = prepare_experiment(D,harmonic_probabilistic_cost,1000*amt_sats)\n",
    "rusty = res = prepare_experiment(D,rusty_proposed_cost,1000*amt_sats,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probabilistic with CLTV successrate: 91.87%\n",
      "probabilistic no CLTV successrate: 91.46%\n",
      "rustyies method successrate: 71.54%\n"
     ]
    }
   ],
   "source": [
    "def can_deliver(path,D,amt):\n",
    "    for s,d in next_hop(path):\n",
    "        if D[s][d][\"balance\"]<amt:\n",
    "            return False\n",
    "    return True\n",
    "\n",
    "def evaluate(graph):\n",
    "    lengths = {\"s\":[],\"f\":[]}\n",
    "    for dest in bos_nodes:\n",
    "        path = nx.dijkstra_path(graph,LN_RENE_PICKHARDT,dest)\n",
    "        \n",
    "        if can_deliver(path,D,amt_sats):\n",
    "            lengths[\"s\"].append(len(path))\n",
    "        else:\n",
    "            lengths[\"f\"].append(len(path))            \n",
    "    return lengths\n",
    "\n",
    "l1 = evaluate(harmonic_with_cltv)\n",
    "print(\"probabilistic with CLTV successrate: {:4.2f}%\".format(100*len(l1[\"s\"])/len(bos_nodes)))\n",
    "l2 = evaluate(harmonic_no_cltv)\n",
    "print(\"probabilistic no CLTV successrate: {:4.2f}%\".format(100*len(l2[\"s\"])/len(bos_nodes)))\n",
    "l3 = evaluate(rusty)\n",
    "print(\"rustyies method successrate: {:4.2f}%\".format(100*len(l3[\"s\"])/len(bos_nodes)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.995575221238938 3.0\n",
      "3.013333333333333 3.0476190476190474\n",
      "6.801136363636363 6.957142857142857\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(l1[\"s\"]), np.mean(l1[\"f\"]))\n",
    "print(np.mean(l2[\"s\"]), np.mean(l2[\"f\"]))\n",
    "print(np.mean(l3[\"s\"]), np.mean(l3[\"f\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
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}