blob: 0fe826e0cb441f91157af6756e231f7c8454498c (plain)

ofs	hex dump	ascii
0000	cb 0d 0d 0a 00 00 00 00 85 fa a7 68 40 27 00 00 e3 00 00 00 00 00 00 00 00 00 00 00 00 07 00 00	...........h@'..................
0020	00 00 00 00 00 f3 b8 00 00 00 97 00 64 00 5a 00 64 01 64 02 6c 01 5a 01 64 01 64 02 6c 02 5a 03	............d.Z.d.d.l.Z.d.d.l.Z.
0040	64 01 64 03 6c 04 6d 05 5a 05 6d 06 5a 06 01 00 64 04 67 01 5a 07 02 00 65 05 64 05 ab 01 00 00	d.d.l.m.Z.m.Z...d.g.Z...e.d.....
0060	00 00 00 00 02 00 65 05 64 06 ab 01 00 00 00 00 00 00 02 00 65 06 64 07 ab 01 00 00 00 00 00 00	......e.d...........e.d.........
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00a0	00 00 00 00 00 00 64 0f 64 0b 84 01 ab 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 ab 00 00 00	......d.d.......................
00c0	00 00 00 00 ab 00 00 00 00 00 00 00 5a 09 64 0c 84 00 5a 0a 64 0d 84 00 5a 0b 64 0e 84 00 5a 0c	............Z.d...Z.d...Z.d...Z.
00e0	79 02 29 10 7a 2e 46 75 6e 63 74 69 6f 6e 73 20 66 6f 72 20 63 6f 6d 70 75 74 69 6e 67 20 73 70	y.).z.Functions.for.computing.sp
0100	61 72 73 69 66 69 65 72 73 20 6f 66 20 67 72 61 70 68 73 2e e9 00 00 00 00 4e 29 02 da 13 6e 6f	arsifiers.of.graphs......N)...no
0120	74 5f 69 6d 70 6c 65 6d 65 6e 74 65 64 5f 66 6f 72 da 0f 70 79 5f 72 61 6e 64 6f 6d 5f 73 74 61	t_implemented_for..py_random_sta
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0160	68 e9 03 00 00 00 da 06 77 65 69 67 68 74 54 29 02 da 0a 65 64 67 65 5f 61 74 74 72 73 da 0d 72	h.......weightT)...edge_attrs..r
0180	65 74 75 72 6e 73 5f 67 72 61 70 68 63 04 00 00 00 00 00 00 00 00 00 00 00 09 00 00 00 03 00 00	eturns_graphc...................
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02c0	7c 04 7a 0b 00 00 ab 02 00 00 00 00 00 00 7d 09 64 03 74 0d 00 00 00 00 00 00 00 00 6a 0e 00 00	|.z...........}.d.t.........j...
02e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 6a 11 00 00 00 00 00 00 00 00 00 00 00 00	................|.j.............
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03c0	00 00 00 00 00 00 00 00 00 00 7c 0d ab 01 00 00 00 00 00 00 01 00 8c 29 04 00 74 13 00 00 00 00	..........|............)..t.....
03e0	00 00 00 00 ab 00 00 00 00 00 00 00 7d 0e 74 13 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00	............}.t.................
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04c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 07 7c 14 66 02 ab 01 00 00 00 00 00 00 01 00 8c 17	..............|.|.f.............
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0580	00 00 00 00 00 00 00 00 00 00 7c 07 7c 17 66 02 ab 01 00 00 00 00 00 00 01 00 7c 15 7c 10 7c 07	..........|.|.f...........|.|.|.
05a0	3c 00 00 00 7c 12 6a 25 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00	<...|.j%........................
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0600	66 02 ab 01 00 00 00 00 00 00 01 00 8c 25 04 00 7c 06 6a 1e 00 00 00 00 00 00 00 00 00 00 00 00	f............%..|.j.............
0620	00 00 00 00 00 00 7c 07 19 00 00 00 44 00 5d 2a 00 00 7d 14 7c 08 7c 14 19 00 00 00 7d 19 7c 12	......|.....D.]*..}.|.|.....}.|.
0640	7c 19 19 00 00 00 7d 1a 7c 19 7c 15 6b 28 00 00 73 06 7c 1a 7c 16 6b 02 00 00 73 01 8c 18 7c 0f	|.....}.|.|.k(..s.|.|.k...s...|.
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0740	8c 0b 7c 0d 7c 10 7c 1c 3c 00 00 00 8c 11 04 00 7c 10 7d 08 7c 06 6a 08 00 00 00 00 00 00 00 00	..|.|.|.<.......|.}.|.j.........
0760	00 00 00 00 00 00 00 00 00 00 44 00 5d 3d 00 00 7d 1b 74 2d 00 00 00 00 00 00 00 00 7c 06 6a 1e	..........D.]=..}.t-........|.j.
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0900	65 74 75 72 6e 73 20 61 20 73 70 61 6e 6e 65 72 20 6f 66 20 74 68 65 20 67 69 76 65 6e 20 67 72	eturns.a.spanner.of.the.given.gr
0920	61 70 68 20 77 69 74 68 20 74 68 65 20 67 69 76 65 6e 20 73 74 72 65 74 63 68 2e 0a 0a 20 20 20	aph.with.the.given.stretch......
0940	20 41 20 73 70 61 6e 6e 65 72 20 6f 66 20 61 20 67 72 61 70 68 20 47 20 3d 20 28 56 2c 20 45 29	.A.spanner.of.a.graph.G.=.(V,.E)
0960	20 77 69 74 68 20 73 74 72 65 74 63 68 20 74 20 69 73 20 61 20 73 75 62 67 72 61 70 68 0a 20 20	.with.stretch.t.is.a.subgraph...
0980	20 20 48 20 3d 20 28 56 2c 20 45 5f 53 29 20 73 75 63 68 20 74 68 61 74 20 45 5f 53 20 69 73 20	..H.=.(V,.E_S).such.that.E_S.is.
09a0	61 20 73 75 62 73 65 74 20 6f 66 20 45 20 61 6e 64 20 74 68 65 20 64 69 73 74 61 6e 63 65 20 62	a.subset.of.E.and.the.distance.b
09c0	65 74 77 65 65 6e 0a 20 20 20 20 61 6e 79 20 70 61 69 72 20 6f 66 20 6e 6f 64 65 73 20 69 6e 20	etween.....any.pair.of.nodes.in.
09e0	48 20 69 73 20 61 74 20 6d 6f 73 74 20 74 20 74 69 6d 65 73 20 74 68 65 20 64 69 73 74 61 6e 63	H.is.at.most.t.times.the.distanc
0a00	65 20 62 65 74 77 65 65 6e 20 74 68 65 0a 20 20 20 20 6e 6f 64 65 73 20 69 6e 20 47 2e 0a 0a 20	e.between.the.....nodes.in.G....
0a20	20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20	...Parameters.....----------....
0a40	20 47 20 3a 20 4e 65 74 77 6f 72 6b 58 20 67 72 61 70 68 0a 20 20 20 20 20 20 20 20 41 6e 20 75	.G.:.NetworkX.graph.........An.u
0a60	6e 64 69 72 65 63 74 65 64 20 73 69 6d 70 6c 65 20 67 72 61 70 68 2e 0a 0a 20 20 20 20 73 74 72	ndirected.simple.graph.......str
0a80	65 74 63 68 20 3a 20 66 6c 6f 61 74 0a 20 20 20 20 20 20 20 20 54 68 65 20 73 74 72 65 74 63 68	etch.:.float.........The.stretch
0aa0	20 6f 66 20 74 68 65 20 73 70 61 6e 6e 65 72 2e 0a 0a 20 20 20 20 77 65 69 67 68 74 20 3a 20 6f	.of.the.spanner.......weight.:.o
0ac0	62 6a 65 63 74 0a 20 20 20 20 20 20 20 20 54 68 65 20 65 64 67 65 20 61 74 74 72 69 62 75 74 65	bject.........The.edge.attribute
0ae0	20 74 6f 20 75 73 65 20 61 73 20 64 69 73 74 61 6e 63 65 2e 0a 0a 20 20 20 20 73 65 65 64 20 3a	.to.use.as.distance.......seed.:
0b00	20 69 6e 74 65 67 65 72 2c 20 72 61 6e 64 6f 6d 5f 73 74 61 74 65 2c 20 6f 72 20 4e 6f 6e 65 20	.integer,.random_state,.or.None.
0b20	28 64 65 66 61 75 6c 74 29 0a 20 20 20 20 20 20 20 20 49 6e 64 69 63 61 74 6f 72 20 6f 66 20 72	(default).........Indicator.of.r
0b40	61 6e 64 6f 6d 20 6e 75 6d 62 65 72 20 67 65 6e 65 72 61 74 69 6f 6e 20 73 74 61 74 65 2e 0a 20	andom.number.generation.state...
0b60	20 20 20 20 20 20 20 53 65 65 20 3a 72 65 66 3a 60 52 61 6e 64 6f 6d 6e 65 73 73 3c 72 61 6e 64	.......See.:ref:`Randomness<rand
0b80	6f 6d 6e 65 73 73 3e 60 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d	omness>`.......Returns.....-----
0ba0	2d 2d 0a 20 20 20 20 4e 65 74 77 6f 72 6b 58 20 67 72 61 70 68 0a 20 20 20 20 20 20 20 20 41 20	--.....NetworkX.graph.........A.
0bc0	73 70 61 6e 6e 65 72 20 6f 66 20 74 68 65 20 67 69 76 65 6e 20 67 72 61 70 68 20 77 69 74 68 20	spanner.of.the.given.graph.with.
0be0	74 68 65 20 67 69 76 65 6e 20 73 74 72 65 74 63 68 2e 0a 0a 20 20 20 20 52 61 69 73 65 73 0a 20	the.given.stretch.......Raises..
0c00	20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 56 61 6c 75 65 45 72 72 6f 72 0a 20 20 20 20 20 20 20	...------.....ValueError........
0c20	20 49 66 20 61 20 73 74 72 65 74 63 68 20 6c 65 73 73 20 74 68 61 6e 20 31 20 69 73 20 67 69 76	.If.a.stretch.less.than.1.is.giv
0c40	65 6e 2e 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 69	en.......Notes.....-----.....Thi
0c60	73 20 66 75 6e 63 74 69 6f 6e 20 69 6d 70 6c 65 6d 65 6e 74 73 20 74 68 65 20 73 70 61 6e 6e 65	s.function.implements.the.spanne
0c80	72 20 61 6c 67 6f 72 69 74 68 6d 20 62 79 20 42 61 73 77 61 6e 61 20 61 6e 64 20 53 65 6e 2c 0a	r.algorithm.by.Baswana.and.Sen,.
0ca0	20 20 20 20 73 65 65 20 5b 31 5d 2e 0a 0a 20 20 20 20 54 68 69 73 20 61 6c 67 6f 72 69 74 68 6d	....see.[1].......This.algorithm
0cc0	20 69 73 20 61 20 72 61 6e 64 6f 6d 69 7a 65 64 20 6c 61 73 20 76 65 67 61 73 20 61 6c 67 6f 72	.is.a.randomized.las.vegas.algor
0ce0	69 74 68 6d 3a 20 54 68 65 20 65 78 70 65 63 74 65 64 0a 20 20 20 20 72 75 6e 6e 69 6e 67 20 74	ithm:.The.expected.....running.t
0d00	69 6d 65 20 69 73 20 4f 28 6b 6d 29 20 77 68 65 72 65 20 6b 20 3d 20 28 73 74 72 65 74 63 68 20	ime.is.O(km).where.k.=.(stretch.
0d20	2b 20 31 29 20 2f 2f 20 32 20 61 6e 64 20 6d 20 69 73 20 74 68 65 0a 20 20 20 20 6e 75 6d 62 65	+.1).//.2.and.m.is.the.....numbe
0d40	72 20 6f 66 20 65 64 67 65 73 20 69 6e 20 47 2e 20 54 68 65 20 72 65 74 75 72 6e 65 64 20 67 72	r.of.edges.in.G..The.returned.gr
0d60	61 70 68 20 69 73 20 61 6c 77 61 79 73 20 61 20 73 70 61 6e 6e 65 72 20 6f 66 20 74 68 65 0a 20	aph.is.always.a.spanner.of.the..
0d80	20 20 20 67 69 76 65 6e 20 67 72 61 70 68 20 77 69 74 68 20 74 68 65 20 73 70 65 63 69 66 69 65	...given.graph.with.the.specifie
0da0	64 20 73 74 72 65 74 63 68 2e 20 46 6f 72 20 77 65 69 67 68 74 65 64 20 67 72 61 70 68 73 20 74	d.stretch..For.weighted.graphs.t
0dc0	68 65 0a 20 20 20 20 6e 75 6d 62 65 72 20 6f 66 20 65 64 67 65 73 20 69 6e 20 74 68 65 20 73 70	he.....number.of.edges.in.the.sp
0de0	61 6e 6e 65 72 20 69 73 20 4f 28 6b 20 2a 20 6e 5e 28 31 20 2b 20 31 20 2f 20 6b 29 29 20 77 68	anner.is.O(k.*.n^(1.+.1./.k)).wh
0e00	65 72 65 20 6b 20 69 73 0a 20 20 20 20 64 65 66 69 6e 65 64 20 61 73 20 61 62 6f 76 65 20 61 6e	ere.k.is.....defined.as.above.an
0e20	64 20 6e 20 69 73 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 6e 6f 64 65 73 20 69 6e 20 47 2e	d.n.is.the.number.of.nodes.in.G.
0e40	20 46 6f 72 20 75 6e 77 65 69 67 68 74 65 64 0a 20 20 20 20 67 72 61 70 68 73 20 74 68 65 20 6e	.For.unweighted.....graphs.the.n
0e60	75 6d 62 65 72 20 6f 66 20 65 64 67 65 73 20 69 73 20 4f 28 6e 5e 28 31 20 2b 20 31 20 2f 20 6b	umber.of.edges.is.O(n^(1.+.1./.k
0e80	29 20 2b 20 6b 6e 29 2e 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d	).+.kn).......References.....---
0ea0	2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 5b 31 5d 20 53 2e 20 42 61 73 77 61 6e 61 2c 20 53 2e 20 53	-------.....[1].S..Baswana,.S..S
0ec0	65 6e 2e 20 41 20 53 69 6d 70 6c 65 20 61 6e 64 20 4c 69 6e 65 61 72 20 54 69 6d 65 20 52 61 6e	en..A.Simple.and.Linear.Time.Ran
0ee0	64 6f 6d 69 7a 65 64 0a 20 20 20 20 41 6c 67 6f 72 69 74 68 6d 20 66 6f 72 20 43 6f 6d 70 75 74	domized.....Algorithm.for.Comput
0f00	69 6e 67 20 53 70 61 72 73 65 20 53 70 61 6e 6e 65 72 73 20 69 6e 20 57 65 69 67 68 74 65 64 20	ing.Sparse.Spanners.in.Weighted.
0f20	47 72 61 70 68 73 2e 0a 20 20 20 20 52 61 6e 64 6f 6d 20 53 74 72 75 63 74 2e 20 41 6c 67 6f 72	Graphs......Random.Struct..Algor
0f40	69 74 68 6d 73 20 33 30 28 34 29 3a 20 35 33 32 2d 35 36 33 20 28 32 30 30 37 29 2e 0a 20 20 20	ithms.30(4):.532-563.(2007).....
0f60	20 e9 01 00 00 00 7a 1a 73 74 72 65 74 63 68 20 6d 75 73 74 20 62 65 20 61 74 20 6c 65 61 73 74	......z.stretch.must.be.at.least
0f80	20 31 e9 02 00 00 00 e9 ff ff ff ff 72 02 00 00 00 29 01 da 03 6b 65 79 29 19 da 0a 56 61 6c 75	.1..........r....)...key)...Valu
0fa0	65 45 72 72 6f 72 da 02 6e 78 da 0b 65 6d 70 74 79 5f 67 72 61 70 68 da 0e 61 64 64 5f 6e 6f 64	eError..nx..empty_graph..add_nod
0fc0	65 73 5f 66 72 6f 6d da 05 6e 6f 64 65 73 da 15 5f 73 65 74 75 70 5f 72 65 73 69 64 75 61 6c 5f	es_from..nodes.._setup_residual_
0fe0	67 72 61 70 68 da 04 6d 61 74 68 da 03 70 6f 77 da 0f 6e 75 6d 62 65 72 5f 6f 66 5f 6e 6f 64 65	graph..math..pow..number_of_node
1000	73 da 03 73 65 74 da 06 76 61 6c 75 65 73 da 06 72 61 6e 64 6f 6d da 03 61 64 64 da 14 5f 6c 69	s..set..values..random..add.._li
1020	67 68 74 65 73 74 5f 65 64 67 65 5f 64 69 63 74 73 da 04 6b 65 79 73 da 03 61 64 6a da 03 6d 69	ghtest_edge_dicts..keys..adj..mi
1040	6e da 03 67 65 74 da 05 69 74 65 6d 73 da 03 6c 65 6e da 14 5f 61 64 64 5f 65 64 67 65 5f 74 6f	n..get..items..len.._add_edge_to
1060	5f 73 70 61 6e 6e 65 72 da 11 72 65 6d 6f 76 65 5f 65 64 67 65 73 5f 66 72 6f 6d da 04 6c 69 73	_spanner..remove_edges_from..lis
1080	74 da 0b 72 65 6d 6f 76 65 5f 65 64 67 65 da 0b 72 65 6d 6f 76 65 5f 6e 6f 64 65 29 1e da 01 47	t..remove_edge..remove_node)...G
10a0	da 07 73 74 72 65 74 63 68 72 09 00 00 00 da 04 73 65 65 64 da 01 6b da 01 48 da 0e 72 65 73 69	..stretchr......seed..k..H..resi
10c0	64 75 61 6c 5f 67 72 61 70 68 da 01 76 da 0a 63 6c 75 73 74 65 72 69 6e 67 da 0b 73 61 6d 70 6c	dual_graph..v..clustering..sampl
10e0	65 5f 70 72 6f 62 da 0a 73 69 7a 65 5f 6c 69 6d 69 74 da 01 69 da 0f 73 61 6d 70 6c 65 64 5f 63	e_prob..size_limit..i..sampled_c
1100	65 6e 74 65 72 73 da 06 63 65 6e 74 65 72 da 0c 65 64 67 65 73 5f 74 6f 5f 61 64 64 da 0f 65 64	enters..center..edges_to_add..ed
1120	67 65 73 5f 74 6f 5f 72 65 6d 6f 76 65 da 0e 6e 65 77 5f 63 6c 75 73 74 65 72 69 6e 67 da 16 6c	ges_to_remove..new_clustering..l
1140	69 67 68 74 65 73 74 5f 65 64 67 65 5f 6e 65 69 67 68 62 6f 72 da 14 6c 69 67 68 74 65 73 74 5f	ightest_edge_neighbor..lightest_
1160	65 64 67 65 5f 77 65 69 67 68 74 da 1b 6e 65 69 67 68 62 6f 72 69 6e 67 5f 73 61 6d 70 6c 65 64	edge_weight..neighboring_sampled
1180	5f 63 65 6e 74 65 72 73 da 08 6e 65 69 67 68 62 6f 72 da 0e 63 6c 6f 73 65 73 74 5f 63 65 6e 74	_centers..neighbor..closest_cent
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1bc0	19 00 00 00 64 01 19 00 00 00 7d 07 7c 06 7c 04 76 01 73 09 7c 07 7c 04 7c 06 19 00 00 00 6b 02	....d.....}.|.|.v.s.|.|.|.....k.
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1c00	7c 04 66 02 53 00 29 02 61 fe 03 00 00 46 69 6e 64 20 74 68 65 20 6c 69 67 68 74 65 73 74 20 65	|.f.S.).a....Find.the.lightest.e
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1fc0	65 20 63 65 6e 74 65 72 20 6f 66 20 74 68 65 20 63 6c 75 73 74 65 72 20 69 73 20 6e 6f 74 20 61	e.center.of.the.cluster.is.not.a
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