Skip to content

Commit e418b39

Browse files
mike-liuliumike-liuliu
committed
m
1 parent bbe561e commit e418b39

3 files changed

+329
-1
lines changed

‎.DS_Store

0 Bytes
Binary file not shown.

‎test Algorithm 1 for solving the widest path problem.ipynb

Lines changed: 328 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,328 @@
1+
{
2+
"cells": [
3+
{
4+
"cell_type": "code",
5+
"execution_count": 1,
6+
"id": "d8c341f4-72ec-41d9-8094-82d124d0d245",
7+
"metadata": {
8+
"scrolled": true
9+
},
10+
"outputs": [],
11+
"source": [
12+
"exec(open(\"./funcs/mmj_cal_functions.py\").read())\n",
13+
"exec(open(\"./funcs/Prim_Minimum_Spanning_Tree.py\").read())\n",
14+
" "
15+
]
16+
},
17+
{
18+
"cell_type": "code",
19+
"execution_count": 2,
20+
"id": "cc47a24e",
21+
"metadata": {},
22+
"outputs": [],
23+
"source": [
24+
"# wides_path_exam_graph, widest path problem example graph, \n",
25+
"# see the upper right graph on https://en.wikipedia.org/wiki/Widest_path_problem\n",
26+
"\n",
27+
"pairwise_bandwidth_matrix = pickle.load( open( \"./data/wides_path_exam_graph.p\", \"rb\" )) \n",
28+
" "
29+
]
30+
},
31+
{
32+
"cell_type": "code",
33+
"execution_count": 3,
34+
"id": "0dc0c24a",
35+
"metadata": {
36+
"scrolled": true
37+
},
38+
"outputs": [
39+
{
40+
"data": {
41+
"text/plain": [
42+
"array([[inf, 15., 53., 0., 0., 0., 0.],\n",
43+
" [15., inf, 40., 0., 0., 46., 0.],\n",
44+
" [53., 40., inf, 17., 31., 0., 0.],\n",
45+
" [ 0., 0., 17., inf, 29., 0., 40.],\n",
46+
" [ 0., 0., 31., 29., inf, 3., 8.],\n",
47+
" [ 0., 46., 0., 0., 3., inf, 11.],\n",
48+
" [ 0., 0., 0., 40., 8., 11., inf]])"
49+
]
50+
},
51+
"execution_count": 3,
52+
"metadata": {},
53+
"output_type": "execute_result"
54+
}
55+
],
56+
"source": [
57+
"pairwise_bandwidth_matrix"
58+
]
59+
},
60+
{
61+
"cell_type": "code",
62+
"execution_count": 4,
63+
"id": "31beb80a",
64+
"metadata": {},
65+
"outputs": [],
66+
"source": [
67+
"graph_nodes_names = {'Dunwich':0, 'Blaxhall':1, 'Harwich':2, 'Clacton':3, 'Tiptree':4, 'Feering':5, 'Maldon':6}\n",
68+
"\n"
69+
]
70+
},
71+
{
72+
"cell_type": "code",
73+
"execution_count": null,
74+
"id": "a630373e",
75+
"metadata": {},
76+
"outputs": [],
77+
"source": []
78+
},
79+
{
80+
"cell_type": "code",
81+
"execution_count": 5,
82+
"id": "74239dd0",
83+
"metadata": {
84+
"scrolled": false
85+
},
86+
"outputs": [
87+
{
88+
"data": {
89+
"text/plain": [
90+
"array([[ 0., 40., 53., 29., 31., 40., 29.],\n",
91+
" [40., 0., 40., 29., 31., 46., 29.],\n",
92+
" [53., 40., 0., 29., 31., 40., 29.],\n",
93+
" [29., 29., 29., 0., 29., 29., 40.],\n",
94+
" [31., 31., 31., 29., 0., 31., 29.],\n",
95+
" [40., 46., 40., 29., 31., 0., 29.],\n",
96+
" [29., 29., 29., 40., 29., 29., 0.]])"
97+
]
98+
},
99+
"execution_count": 5,
100+
"metadata": {},
101+
"output_type": "execute_result"
102+
}
103+
],
104+
"source": [
105+
"Widest_path_matrix_algo_4 = cal_Widest_path_problem_matrix_by_algo_4(pairwise_bandwidth_matrix)\n",
106+
"Widest_path_matrix_algo_4\n",
107+
"\n"
108+
]
109+
},
110+
{
111+
"cell_type": "code",
112+
"execution_count": 6,
113+
"id": "1567b10d",
114+
"metadata": {},
115+
"outputs": [
116+
{
117+
"data": {
118+
"text/plain": [
119+
"29.0"
120+
]
121+
},
122+
"execution_count": 6,
123+
"metadata": {},
124+
"output_type": "execute_result"
125+
}
126+
],
127+
"source": [
128+
"i = graph_nodes_names[\"Maldon\"]\n",
129+
"j = graph_nodes_names[\"Feering\"]\n",
130+
"\n",
131+
"Widest_path_matrix_algo_4[i,j]\n"
132+
]
133+
},
134+
{
135+
"cell_type": "code",
136+
"execution_count": 7,
137+
"id": "fd13e1fe",
138+
"metadata": {},
139+
"outputs": [],
140+
"source": [
141+
"N = len(pairwise_bandwidth_matrix)\n",
142+
"for i in range(N):\n",
143+
" Widest_path_matrix_algo_4[i,i] = np.inf"
144+
]
145+
},
146+
{
147+
"cell_type": "code",
148+
"execution_count": 8,
149+
"id": "f405f107",
150+
"metadata": {},
151+
"outputs": [
152+
{
153+
"data": {
154+
"text/plain": [
155+
"array([[inf, 40., 53., 29., 31., 40., 29.],\n",
156+
" [40., inf, 40., 29., 31., 46., 29.],\n",
157+
" [53., 40., inf, 29., 31., 40., 29.],\n",
158+
" [29., 29., 29., inf, 29., 29., 40.],\n",
159+
" [31., 31., 31., 29., inf, 31., 29.],\n",
160+
" [40., 46., 40., 29., 31., inf, 29.],\n",
161+
" [29., 29., 29., 40., 29., 29., inf]])"
162+
]
163+
},
164+
"execution_count": 8,
165+
"metadata": {},
166+
"output_type": "execute_result"
167+
}
168+
],
169+
"source": [
170+
"Widest_path_matrix_algo_4"
171+
]
172+
},
173+
{
174+
"cell_type": "code",
175+
"execution_count": 9,
176+
"id": "c1f29450",
177+
"metadata": {},
178+
"outputs": [],
179+
"source": [
180+
"# See Section 7 (SOLVING THE WIDEST PATH PROBLEM) of the paper:\n",
181+
"# https://arxiv.org/abs/2301.05994\n",
182+
"\n",
183+
"def wpp_n_to_r(distance_matrix, widest_path_matrix, n, r):\n",
184+
" max_jump_list = []\n",
185+
" for ttt in range(n):\n",
186+
" m_jump = np.min((distance_matrix[n,ttt],widest_path_matrix[ttt,r]))\n",
187+
" max_jump_list.append(m_jump)\n",
188+
" return np.max(max_jump_list)\n",
189+
"\n",
190+
"def wpp_r_to_n(distance_matrix, widest_path_matrix, n, r):\n",
191+
" max_jump_list = []\n",
192+
" for ttt in range(n):\n",
193+
" m_jump = np.min((widest_path_matrix[r,ttt], distance_matrix[ttt, n]))\n",
194+
" max_jump_list.append(m_jump)\n",
195+
" return np.max(max_jump_list)\n",
196+
"\n",
197+
" \n",
198+
"def cal_n_wpp(distance_matrix, widest_path_matrix, n):\n",
199+
" for i in range(n):\n",
200+
" widest_path_matrix[n,i] = wpp_n_to_r(distance_matrix, widest_path_matrix, n, i)\n",
201+
" widest_path_matrix[i,n] = wpp_r_to_n(distance_matrix, widest_path_matrix, n, i)\n",
202+
" \n",
203+
" for i in range(n): \n",
204+
" for j in range(n):\n",
205+
" if i < j:\n",
206+
" widest_path_matrix[i,j] = update_wpp_ij(distance_matrix, widest_path_matrix, n, i, j)\n",
207+
" widest_path_matrix[j,i] = update_wpp_ij(distance_matrix, widest_path_matrix, n, j, i)\n",
208+
" \n",
209+
"def update_wpp_ij(distance_matrix, widest_path_matrix, n, i,j):\n",
210+
" m1 = widest_path_matrix[i,j]\n",
211+
" m2 = np.min((widest_path_matrix[i,n],widest_path_matrix[n,j]))\n",
212+
" return np.max((m1,m2))\n",
213+
"\n",
214+
"def cal_widest_path_matrix_algo_1_python(distance_matrix):\n",
215+
" \n",
216+
" N = len(distance_matrix)\n",
217+
" \n",
218+
" widest_path_matrix = np.ones((N,N))*np.inf\n",
219+
"\n",
220+
" widest_path_matrix[0,1] = distance_matrix[0,1]\n",
221+
" widest_path_matrix[1,0] = distance_matrix[1,0]\n",
222+
" \n",
223+
" for kk in range(2, N):\n",
224+
" cal_n_wpp(distance_matrix, widest_path_matrix, kk)\n",
225+
" return widest_path_matrix"
226+
]
227+
},
228+
{
229+
"cell_type": "code",
230+
"execution_count": 10,
231+
"id": "2fdb1448",
232+
"metadata": {},
233+
"outputs": [
234+
{
235+
"data": {
236+
"text/plain": [
237+
"array([[inf, 40., 53., 29., 31., 40., 29.],\n",
238+
" [40., inf, 40., 29., 31., 46., 29.],\n",
239+
" [53., 40., inf, 29., 31., 40., 29.],\n",
240+
" [29., 29., 29., inf, 29., 29., 40.],\n",
241+
" [31., 31., 31., 29., inf, 31., 29.],\n",
242+
" [40., 46., 40., 29., 31., inf, 29.],\n",
243+
" [29., 29., 29., 40., 29., 29., inf]])"
244+
]
245+
},
246+
"execution_count": 10,
247+
"metadata": {},
248+
"output_type": "execute_result"
249+
}
250+
],
251+
"source": [
252+
"Widest_path_matrix_algo_1 = cal_widest_path_matrix_algo_1_python(pairwise_bandwidth_matrix)\n",
253+
"Widest_path_matrix_algo_1"
254+
]
255+
},
256+
{
257+
"cell_type": "code",
258+
"execution_count": 11,
259+
"id": "5cd76527",
260+
"metadata": {},
261+
"outputs": [
262+
{
263+
"data": {
264+
"text/plain": [
265+
"29.0"
266+
]
267+
},
268+
"execution_count": 11,
269+
"metadata": {},
270+
"output_type": "execute_result"
271+
}
272+
],
273+
"source": [
274+
"i = graph_nodes_names[\"Maldon\"]\n",
275+
"j = graph_nodes_names[\"Feering\"]\n",
276+
"\n",
277+
"Widest_path_matrix_algo_1[i,j]"
278+
]
279+
},
280+
{
281+
"cell_type": "code",
282+
"execution_count": 12,
283+
"id": "658d4389",
284+
"metadata": {},
285+
"outputs": [
286+
{
287+
"name": "stdout",
288+
"output_type": "stream",
289+
"text": [
290+
"True\n"
291+
]
292+
}
293+
],
294+
"source": [
295+
"print(np.allclose(Widest_path_matrix_algo_1, Widest_path_matrix_algo_4))\n"
296+
]
297+
},
298+
{
299+
"cell_type": "code",
300+
"execution_count": null,
301+
"id": "8e0b76a7",
302+
"metadata": {},
303+
"outputs": [],
304+
"source": []
305+
}
306+
],
307+
"metadata": {
308+
"kernelspec": {
309+
"display_name": "Python 3 (ipykernel)",
310+
"language": "python",
311+
"name": "python3"
312+
},
313+
"language_info": {
314+
"codemirror_mode": {
315+
"name": "ipython",
316+
"version": 3
317+
},
318+
"file_extension": ".py",
319+
"mimetype": "text/x-python",
320+
"name": "python",
321+
"nbconvert_exporter": "python",
322+
"pygments_lexer": "ipython3",
323+
"version": "3.12.3"
324+
}
325+
},
326+
"nbformat": 4,
327+
"nbformat_minor": 5
328+
}

‎test Algorithm 4 for solving the Widest path problem.ipynb

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -23,7 +23,7 @@
2323
"# wides_path_exam_graph, widest path problem example graph, \n",
2424
"# see the upper right graph on https://en.wikipedia.org/wiki/Widest_path_problem\n",
2525
"\n",
26-
"pairwise_bandwidth_matrix = pickle.load( open( \"./wides_path_exam_graph.p\", \"rb\" )) \n",
26+
"pairwise_bandwidth_matrix = pickle.load( open( \"./data/wides_path_exam_graph.p\", \"rb\" )) \n",
2727
" "
2828
]
2929
},

0 commit comments

Comments
 (0)