hSrSSKrSSKJr SSKJr SS/rSrSr\"S 5\"S 5\RS 555r \"S 5\"S 5\RS S j555r g)acRoutines to calculate the broadcast time of certain graphs. Broadcasting is an information dissemination problem in which a node in a graph, called the originator, must distribute a message to all other nodes by placing a series of calls along the edges of the graph. Once informed, other nodes aid the originator in distributing the message. The broadcasting must be completed as quickly as possible subject to the following constraints: - Each call requires one unit of time. - A node can only participate in one call per unit of time. - Each call only involves two adjacent nodes: a sender and a receiver. N) NetworkXError)not_implemented_fortree_broadcast_centertree_broadcast_timec^[[URU55U-TRSS9n[ U4Sj[ USS955$)NTkeyreversec38># UHupTUU-v M g7fN).0iuvaluess R/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/broadcasting.py +_get_max_broadcast_value..sA)@vay1})@sstart)sortedset neighborsgetmax enumerate)GUvradjs ` r_get_max_broadcast_valuer"s? Q[[^$q(fjj$ GC A3a)@A AAc^^[URU5TRSS9n[UU4Sj[ USS955n[ U/USU-5$)NTrc3H># UHupTUU-T:XdMUv M g7fr r )rrrtargetrs rr)_get_broadcast_centers.. s& N241fQi!mv6MQQ2s" "rr)rrrnextrr)rr rr&r!js `` r_get_broadcast_centersr*sK QVZZ >C N9S2 NNA sS!W} r#directed multigraphc x^^ [R"T5(d [S5 TR5S:XaS[ TR 554$TR5S:XaS[ TR 554$TR VVs1sHupUS:XdM UiM nnnUVs0sHoDS_M snm TR5nURU5 UR VVs1sHupUS:XdM UiM nnnT RU4SjU55 UR5S:a[UU 4SjS9n[URU55nURU5 URU5 URU5 UR U5S:Xa/T RU[!TX8T 505 URU5 UR5S:aM[R"R%U5n[!TX8T 5n U ['TUT U 54$s snnfs snfs snnf)uReturn the Broadcast Center of the tree `G`. The broadcast center of a graph G denotes the set of nodes having minimum broadcast time [1]_. This is a linear algorithm for determining the broadcast center of a tree with ``N`` nodes, as a by-product it also determines the broadcast time from the broadcast center. Parameters ---------- G : undirected graph The graph should be an undirected tree Returns ------- BC : (int, set) tuple minimum broadcast number of the tree, set of broadcast centers Raises ------ NetworkXNotImplemented If the graph is directed or is a multigraph. References ---------- .. [1] Slater, P.J., Cockayne, E.J., Hedetniemi, S.T, Information dissemination in trees. SIAM J.Comput. 10(4), 692–701 (1981) zInput graph is not a treerrc3J># UHoTRUS- 4v M g7f)rN)degree)rwrs rr(tree_broadcast_center..Ts 21ahhqkAo&s #c>TU$r r )nrs r'tree_broadcast_center..Ys r#)r )nxis_treernumber_of_nodesrnodesr0copyremove_nodes_fromupdateminr(raddremove remove_noder"utilsarbitrary_elementr*) rnodedegrr4TWr1r b_Trs ` @rrr$s@ ::a==12a#aggi.  a#aggi.   !xx4x)$3!8xA4 AqdA F A !xx4x)$3!8xA4 MM222    " * + Q  a   a 88A;!  MM16q!GH I EE!H    "" ""1%A "1aF 3C &q!VS9 99; 5  5s H+&H+3 H12 H6H6cX^^[T5up#TbU[UU4SjU55-$[RT[ T55nUH?n[ R "TU5R5HupgXtU:dMXtU'M MA U[UR55-$)aReturn the Broadcast Time of the tree `G`. The minimum broadcast time of a node is defined as the minimum amount of time required to complete broadcasting starting from the originator. The broadcast time of a graph is the maximum over all nodes of the minimum broadcast time from that node [1]_. This function returns the minimum broadcast time of `node`. If `node` is None the broadcast time for the graph is returned. Parameters ---------- G : undirected graph The graph should be an undirected tree node: int, optional index of starting node. If `None`, the algorithm returns the broadcast time of the tree. Returns ------- BT : int Broadcast Time of a node in a tree Raises ------ NetworkXNotImplemented If the graph is directed or is a multigraph. References ---------- .. [1] Harutyunyan, H. A. and Li, Z. "A Simple Construction of Broadcast Graphs." In Computing and Combinatorics. COCOON 2019 (Ed. D. Z. Du and C. Tian.) Springer, pp. 240-253, 2019. c3T># UHn[R"TTU5v M g7fr )r7shortest_path_length)rrrrDs rr&tree_broadcast_time..s#Jc00D!<dictfromkeyslenr7rKitemsrr)rrDrHb_Cdist_from_centerrr dists`` rrrmsL%Q'HC SJcJJJJ}}QA/ ..q!4::rYs ".  B  Z \"C:#!C:LZ \"+0#!+0r#