ܛ7indZddlZddlmZddgZdZdZeded ejd Z eded ejd d Z y) 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)not_implemented_fortree_broadcast_centertree_broadcast_timectt|j||zjd}t fdt |dDS)NTkeyreversec34K|]\}}||zywN).0iuvaluess ]/home/rose/Desktop/poly/venv/lib/python3.12/site-packages/networkx/algorithms/broadcasting.py z+_get_max_broadcast_value..s A)@Avay1})@sstart)sortedset neighborsgetmax enumerate)GUvradjs ` r_get_max_broadcast_valuer s? Q[[^$q(fjj$ GC A3a)@A AAct|j|jd}tfdt |dD}t |g|d|zS)NTrc3@K|]\}}||zk(s|ywr r )r rrtargetrs rrz)_get_broadcast_centers..s' N241afQi!mv6MQ2srr)rrrnextrr)rrrr$rjs `` r_get_broadcast_centersr'sK QVZZ >C N9S2 NNA sS!W} r!directed multigraphc tjstjdtx}dkr|dz t fSj Dchc] \}}|dk(s |}}}|Dcic]}|d}}j }|j||j Dchc] \}}|dk(s |}}}|jfd|Dt|dk\rt||j}t|j|} |j||j||j||j | dk(r0|j| t!|| |i|j| t|dk\rtj"j%|} t!|| |} | t'| || fScc}}wcc}wcc}}w)uReturn the broadcast center of a tree. The broadcast center of a graph `G` denotes the set of nodes having minimum broadcast time [1]_. This function implements 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 : Graph The graph should be an undirected tree. Returns ------- b_T, b_C : (int, set) tuple Minimum broadcast time of the broadcast center in `G`, set of nodes in the broadcast center. Raises ------ NetworkXNotImplemented If `G` is directed or is a multigraph. NotATree If `G` is not a tree. References ---------- .. [1] Slater, P.J., Cockayne, E.J., Hedetniemi, S.T, Information dissemination in trees. SIAM J.Comput. 10(4), 692–701 (1981) zG is not a treerrc3FK|]}|j|dz fywrN)degree)r wrs rrz(tree_broadcast_center..Us#211ahhqkAo&s!)r)nxis_treeNotATreelenrr.copyremove_nodes_fromupdateminrr%raddremove remove_noder utilsarbitrary_elementr') rnnodedegrrTWr/rb_Ts ` rrr#sH ::a=kk+,, V q1uc!f} !xx4x)$3!8xA4 AqadAF  A !xx4x)$3!8xA4 MM222 a&A+ vzz " Q  a   a 88A;!  MM16q!QGH I EE!H a&A+" ""1%A "1aF 3C &q!VS9 99; 5  5s G!)G!4 G'0 G,>G,c &|vrdd}tj|t|\}},|tdtj||Dzdz S|t fdt tj||DzS)aReturn the minimum broadcast time of a (node in a) tree. The minimum broadcast time of a node is defined as the minimum amount of time required to complete broadcasting starting from that node. 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 : Graph The graph should be an undirected tree. node : node, optional (default=None) Starting node for the broadcasting. If `None`, the algorithm returns the broadcast time of the graph instead. Returns ------- int Minimum broadcast time of `node` in `G`, or broadcast time of `G` if no node is provided. Raises ------ NetworkXNotImplemented If `G` is directed or is a multigraph. NodeNotFound If `node` is not a node in `G`. NotATree If `G` is not a tree. 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. znode z not in Gc3 K|]}dywr-r )r _s rrz&tree_broadcast_time..s:$9q$9s rc32K|]\}}|vs |ywr r )r dlayerr?s rrz&tree_broadcast_time..s :hadem:s )r1 NodeNotFoundrsum bfs_layersr%r)rr?errrCb_Cs ` rrrns\ DMdV9%ooc""$Q'HC |S:BMM!S$9:::Q>> #BMM!S$9: r!r ) __doc__networkxr1networkx.utilsr__all__r r' _dispatchablerrr r!rrTs .  B  Z \"E:#!E:PZ \"3#!3r!