[1] Dennis Abts. “The Cray XT4 and Seastar 3-D torus interconnect”. In: (2011).

[2] Narasimha R Adiga, Matthias A Blumrich, Dong Chen, Paul Coteus, Alan Gara, Mark E Giampapa, Philip Heidelberger, Sarabjeet Singh, Burkhard D Steinmacher- Burow, Todd Takken, et al. “Blue Gene/L torus interconnection network”. In: IBM Journal of Research and Development 49.2.3 (2005), pp. 265–276.

[3] R Ahlswede, H Haroutunian, and L Khachatrian. Messy broadcasting in networks, Communications and Cryptography, eds. RE Blahut, DJ Costello Jr., U. Mauter, and T. Mittelholzer. 1994.

[4] Stefan Arnborg, Jens Lagergren, and Detlef Seese. “Easy problems for tree-decomposable graphs”. In: Journal of Algorithms 12.2 (1991), pp. 308–340.

[5] Baruch Awerbuch, Oded Goldreich, David Peleg, and Ronen Vainish. “A tradeoff between information and communication in broadcast protocols”. In: Aegean Workshop on Computing. Springer. 1988, pp. 369–379.

[6] Anindo Bagchi and S. Louis Hakimi. “Data transfers in broadcast networks”. In: IEEE Computer Architecture Letters 41.07 (1992), pp. 842–847.

[7] Anindo Bagchi, S. Louis Hakimi, and Edward F. Schmeichel. “Gossiping in a distributed network”. In: IEEE transactions on computers 42.2 (1993), pp. 253–256.

[8] Amotz Bar-Noy, Sudipto Guha, Joseph Naor, and Baruch Schieber. “Multicasting in heterogeneous networks”. In: Proceedings of the thirtieth annual ACM symposium on Theory of computing. 1998, pp. 448–453.

[9] Reuven Bar-Yehuda, Amos Israeli, and Alon Itai. “Multiple communication in multihop radio networks”. In: SIAM Journal on Computing 22.4 (1993), pp. 875–887.

[10] René Beier and Jop F. Sibeyn. “A powerful heuristic for telephone gossiping”. In:
SIROCCO 7, Proceedings of the 7th International Colloquium on Structural Information and Communication Complexity, Laquila, Italy, June 20-22, 2000. Ed. by Michele Flammini, Enrico Nardelli, Guido Proietti, and Paul G. Spirakis. Carleton Scientific, 2000, pp. 17–35.

[11] Amir Ben-Dor, Shai Halevi, and Assaf Schuster. On greedy hot-potato routing. Laboratory for Parallel Computing Research, Technion-Israel Institute of . . ., 1993.

[12] Jean-Claude Bermond, Pierre Fraigniaud, and Joseph G Peters. “Antepenultimate broadcasting”. In: Networks 26.3 (1995), pp. 125–137.

[13] Jean-Claude Bermond, Pavol Hell, Arthur L Liestman, and Joseph G Peters. “Broadcasting in bounded degree graphs”. In: SIAM Journal on Discrete Mathematics 5.1 (1992), pp. 10–24.

[14] Jean-Claude Bermond and Claudine Peyrat. “Broascasting in de Bruijn networks”. In: Congressus numerantium 66 (1988), pp. 283–292.

[15] Jean-Claude Bermond and Claudine Peyrat. “De Bruijn and Kautz networks: a competitor for the hypercube?” In: First European Workshop on Hypercube and Distributed Computers. Elsevier. 1989, pp–279.

[16] Dimitri P Bertsekas, C Özveren, George D Stamoulis, Paul Tseng, and John N. Tsit- siklis. “Optimal communication algorithms for hypercubes”. In: Journal of Parallel and Distributed Computing 11.4 (1991), pp. 263–275.

[17] Puspal Bhabak and Hovhannes A. Harutyunyan. “Constant Approximation for Broadcasting in k-cycle Graph”. In: Conference on Algorithms and Discrete Applied Mathematics. Springer. 2015, pp. 21–32.

[18] Laxmi N. Bhuyan and Dharma P. Agrawal. “Generalized hypercube and hyperbus structures for a computer network”. In: IEEE Computer Architecture Letters 33.04 (1984), pp. 323–333.

[19] Luc Bomans and Dirk Roose. “Communication benchmarks on the iPSC/2”. In:
Proceedings of the First European Workshop on Hypercube and Distributed Computers. 1989, pp. 93–103.

[20] Jehoshua Bruck, Robert Cypher, and Ching-Tien Ho. Multiple message broadcasting with generalized Fibonacci trees. IEEE, 1992.

[21] Renato M Capocelli, Luisa Gargano, and Ugo Vaccaro. “Time bounds for broadcasting in bounded degree graphs”. In: International Workshop on Graph-Theoretic Concepts in Computer Science. Springer. 1989, pp. 19–33.

[22] MajaCˇevnikandJanezŽerovnik “Broadcasting on cactus graphs”.In: Journal of Combinatorial Optimization 33.1 (2017), pp. 292–316.

[23] T Champion and B Tourancheau. “Tnode: user document”. In: Technical Report LIP-IMAG 89-02. Ecole Normale Supérieure de Lyon France, 1989.

[24] Siu-Cheung Chau and Arthur L Liestman. “Constructing minimal broadcast networks”. In: J. Combin. Inform. Syst. Sci 10 (1985), pp. 110–122.

[25] X Chen. “An upper bound for the broadcast function B (n), Chinese J”. In: Computers 13 (1990), pp. 605–611.

[26] Edward Chow, Herbert Madan, John Peterson, Dirk Grunwald, and Daniel Reed. “Hyperswitch network for the hypercube computer”. In: ACM SIGARCH Computer Architecture News 16.2 (1988), pp. 90–99.

[27] Israel Cidon and Inder S Gopal. “Paris: An approach to integrated high-speed private networks”. In: International Journal of Digital & Analog Cabled Systems 1.2 (1988), pp. 77–85.

[28] D Clark, B Davie, D Farber, I Gopal, and B Kadaba. “D, Sincoskie, J. Smith, and D. Tennenhouse, The AURORA gigabit testbed”. In: Computer Networks and ISDN (1991).

[29] EJ Cockayne and ST Hedetniemi. A conjecture concerning broadcasting in m- dimensional grid graphs. Tech. rep. Technical Report CS-TR-78-14, University of Oregon, 1978.

[30] Francesc Comellas, Hovhannes A. Harutyunyan, and Arthur L Liestman. “Messy broadcasting in multidimensional directed tori”. In: Journal of Interconnection Networks 4.01 (2003), pp. 37–51.

[31] Kris Coolsaet, H De Meyer, and Veerle Fack. “Optimal algorithms for total ex- change without buffering on the hypercube”. In: BIT Numerical Mathematics 32.4 (1992), pp. 559–569.

[32] David Culler, Richard Karp, David Patterson, Abhijit Sahay, Klaus Erik Schauser, Eunice Santos, Ramesh Subramonian, and Thorsten Von Eicken. “LogP: Towards a realistic model of parallel computation”. In: Proceedings of the fourth ACM SIG- PLAN symposium on Principles and practice of parallel programming. 1993, pp. 1– 12.

[33] William J Dally. “Performance analysis of k-ary n-cube interconnection networks”. In: IEEE transactions on Computers 39.06 (1990), pp. 775–785.

[34] William J Dally, Andrew Chien, Stuart Fiske, Waldemar Horwat, and John Keen. The J-machine: A fine grain concurrent computer. Tech. rep. Massachusetts inst of tech Cambridge microsystems research enter, 1989.

[35] Michael J Dinneen, Michael R Fellows, and Vance Faber. “Algebraic constructions of efficient broadcast networks”. In: International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes. Springer. 1991, pp. 152–158.

[36] Michael J Dinneen, Jose A Ventura, Mark C Wilson, and Golbon Zakeri. “Compound constructions of broadcast networks”. In: Discrete applied mathematics 93.2- 3 (1999), pp. 205–232.

[37] S. Djelloul. “Etudes de certains rCseaux d’interconnexion: structures et communi- cations”. PhD thesis. Paris-Sud, Orsay, 1992.

[38] Michael Elkin and Guy Kortsarz. “Sublogarithmic approximation for telephone multicast: path out of jungle.” In: SODA. Vol. 3. 2003, pp. 76–85.

[39] Michael Elkin and Guy Kortsarz. “A combinatorial logarithmic approximation algorithm for the directed telephone broadcast problem”. In: SIAM journal on Computing 35.3 (2005), pp. 672–689.

[40] AM Farley and ST Hedetniemi. “Broadcasting in grid graphs”. In: Proc. 9th SE Conf. Combinatorics, Graph Theory, and Computing, Utilitas Mathematica. 1978, pp. 275–288.

[41] Arthur Farley, Stephen Hedetniemi, Sandra Mitchell, and Andrzej Proskurowski. “Minimum broadcast graphs”. In: Discrete Mathematics 25.2 (1979), pp. 189–193.

[42] Arthur M Farley and Andrzej Proskurowski. Broadcasting: Between whispering and shouting. University of Oregon. Department of Computer and Information Science, 1989.

[43] Uriel Feige, David Peleg, Prabhakar Raghavan, and Eli Upfal. “Randomized broadcast in networks”. In: Random Structures & Algorithms 1.4 (1990), pp. 447–460.

[44] Pierre Fraigniaud. “Complexity analysis of broadcasting in hypercubes with restricted communication capabilities”. In: Journal of Parallel and Distributed Computing 16.1 (1992), pp. 15–26.

[45] Pierre Fraigniaud and Emmanuel Lazard. “Methods and problems of communication in usual networks”. In: Discrete Applied Mathematics 53.1-3 (1994), pp. 79– 133.

[46] Pierre Fraigniaud and Emmanuel Lazard. “Methods and problems of communication in usual networks”. In: Discrete Applied Mathematics 53.1-3 (1994), pp. 79– 133.

[47] Pierre Fraigniaud and Sandrine Vial. “Approximation algorithms for broadcasting and gossiping”. In: Journal of Parallel and Distributed Computing 43.1 (1997), pp. 47–55.

[48] Pierre Fraigniaud and Sandrine Vial. “Comparison of heuristics for one-to-all and all-to-all communications in partial meshes”. In: Parallel Processing Letters 9.01 (1999), pp. 9–20.

[49] Matthias Függer, Thomas Nowak, and Kyrill Winkler. “On the radius of nonsplit graphs and information dissemination in dynamic networks”. In: Discrete Applied Mathematics 282 (2020), pp. 257–264.

[50] Luisa Gargano and Ugo Vaccaro. “On the construction of minimal broadcast networks”. In: Networks 19.6 (1989), pp. 673–689.

[51] Jonathan L Gross, Jay Yellen, and Ping Zhang. Handbook of graph theory. CRC press, 2013.

[52] András Hajnal, Eric C Milner, and Endre Szemerédi. “A cure for the telephone disease”. In: Canadian Mathematical Bulletin 15.3 (1972), pp. 447–450.

[53] Hovhannes A. Harutyunyan, George Laza, and Edward Maraachlian. “Broadcasting in necklace graphs”. In: Proceedings of the 2nd Canadian Conference on Computer Science and Software Engineering. 2009, pp. 253–256.

[54] Hovhannes A. Harutyunyan and Arthur L Liestman. “Messy broadcasting”. In: Parallel Processing Letters 8.02 (1998), pp. 149–159.

[55] Hovhannes A. Harutyunyan and Arthur L Liestman. “More broadcast graphs”. In: Discrete Applied Mathematics 98.1-2 (1999), pp. 81–102.

[56] Hovhannes A. Harutyunyan and Edward Maraachlian. “Linear algorithm for broadcasting in unicyclic graphs”. In: International Computing and Combinatorics Conference. Springer. 2007, pp. 372–382.

[57] Hovhannes A. Harutyunyan and Edward Maraachlian. “On broadcasting in uni- cyclic graphs”. In: Journal of combinatorial optimization 16.3 (2008), pp. 307– 322.

[58] Hovhannes A. Harutyunyan and Edward Maraachlian. “Broadcasting in fully connected trees”. In: 2009 15th International Conference on Parallel and Distributed Systems. IEEE. 2009, pp. 740–745.

[59] Hovhannes A. Harutyunyan and Edward Maraachlian. “Linear Algorithm for Broadcasting in Networks With No Intersecting Cycles.” In: PDPTA. 2009, pp. 296–301.

[60] Hovhannes A. Harutyunyan and Edward Maraachlian. “Broadcasting in hierarchical tree cluster network”. In: PDPTA 2010: proceedings of the 2010 international conference on parallel and distributed processing techniques and applications (Las Vegas NV, July 12-15, 2010). 2010, pp. 479–484.

[61] Hovhannes A. Harutyunyan and Bin Shao. “An efficient heuristic for broadcasting in networks”. In: Journal of Parallel and Distributed Computing 66.1 (2006), pp. 68–76.

[62] Sandra M Hedetniemi, Stephen T Hedetniemi, and Arthur L Liestman. “A survey of gossiping and broadcasting in communication networks”. In: Networks 18.4 (1988), pp. 319–349.

[63] Marie-Claude Heydemann, Jaroslav Opatrny, and Dominique Sotteau. “Broadcasting and spanning trees in de Bruijn and Kautz networks”. In: Discrete applied mathematics 37 (1992), pp. 297–317.

[64] JurajHromkovicˇ,Claus-DieterJeschke,andBurkhardMonien.“Optimalalgo- rithms for dissemination of information in some interconnection networks”. In: International Symposium on Mathematical Foundations of Computer Science. Springer. 1990, pp. 337–346.

[65] Juraj Hromkovicˇ, Ralf Klasing, Burkhard Monien, and Regine Peine. “Dissemination of information in interconnection networks (broadcasting & gossiping)”. In: Combinatorial network theory. Springer, 1996, pp. 125–212.

[66] Cray Inc. The Gemini Network. URL: https : / / wiki . alcf . anl . gov / parts/images/2/2c/Gemini-whitepaper.pdf.

[67] Andreas Jakoby, Rüdiger Reischuk, and Christian Schindelhauer. “The complexity of broadcasting in planar and decomposable graphs”. In: Discrete Applied Mathe- matics 83.1-3 (1998), pp. 179–206.

[68] Klaus Jansen and Haiko Müller. “The minimum broadcast time problem for several processor networks”. In: Theoretical Computer Science 147.1-2 (1995), pp. 69–85.

[69] LH Khachatrian and OS Harutounian. “Construction of new classes of minimal broadcast networks”. In: Conference on Coding Theory, Armenia. 1990, pp. 69–77.

[70] Ralf Klasing, Burkhard Monien, Regine Peine, and Elena A Stöhr. “Broadcasting in butterfly and DeBruijn networks”. In: Discrete Applied Mathematics 53.1-3 (1994), pp. 183–197.

[71] C Ko. “Broadcasting, Graph homomorphisms and chord intersections.” In: (1980).

[72] Chen-Shung Ko. “On a conjecture concerning broadcasting in grid graphs”. In: AMS Notices (1979), A196–A197.

[73] Guy Kortsarz and David Peleg. “Approximation algorithms for minimum time broadcast”. In: Israel Symposium on Theory of Computing and Systems. Springer. 1992, pp. 67–78.

[74] S Kuppuswami and B Tourancheau. “Evaluating the performances of transputer based hypercube vector computer”. In: La lettre du Transputer 4 (1990).

[75] Roger Labahn. “Information flows on hypergraphs”. In: Discrete mathematics 113.1- 3 (1993), pp. 71–97.

[76] Roger Labahn. “A minimum broadcast graph on 63 vertices”. In: Discrete Applied Mathematics 53.1-3 (1994), pp. 247–250.

[77] Tomas Lang and Harold S Stone. “A shuffle-exchange network with simplified control”. In: IEEE Transactions on computers 100.1 (1976), pp. 55–65.

[78] Frank Thomson Leighton. Layouts for the Shuffle-Exchange Graph and Lower Bound Techniques for VLSI. Tech. rep. Massachusetts inst of tech Cambridge lab for computer science, 1982.

[79] Arthur L Liestman and Joseph G Peters. “Broadcast networks of bounded degree”. In: SIAM journal on Discrete Mathematics 1.4 (1988), pp. 531–540.

[80] Arthur L Liestman and Joseph G Peters. “Minimum broadcast digraphs”. In: Discrete Applied Mathematics 37 (1992), pp. 401–419.

[81] Arthur L. Liestman and Dana Richards. “Network communication in edge-colored graphs: gossiping”. In: IEEE Transactions on Parallel and Distributed Systems 4.4 (1993), pp. 438–445.

[82] Philip D MacKenzie. “A lower bound for order-preserving broadcast in the postal model”. In: Parallel Processing Letters 3.04 (1993), pp. 313–320.

[83] David May. “The next generation transputers and beyond”. In: European Conference on Distributed Memory Computing. Springer. 1991, pp. 7–22.

[84] DS Meliksetian and CYR Chen. Optimal routing algorithm and other communication issues of the cube-connected cycles. Tech. rep. Tech. Rep. TR90-4, Dept. Elec. & Comp. Eng., Syracuse University, 1990.

[85] Martin Middendorf. “Minimum broadcast time is NP-complete for 3-regular planar graphs and deadline 2”. In: Information Processing Letters 46.6 (1993), pp. 281– 287.

[86] Sandra Mitchell and Stephen Hedetniemi. “A census of minimum broadcast graphs”. In: J. Combin. Inform. System Sci 5 (1980), pp. 141–151.

[87] Mohamed Ould-Khaoua. “On the optimal network for multicomputer: Torus or hypercube?” In: European Conference on Parallel Processing. Springer. 1998, pp. 989– 992.

[88] Brigitte Plateau and Denis Trystam. “Optimal total exchange for a 3-D torus of processors”. In: Information Processing Letters 42.2 (1992), pp. 95–102.

[89] Franco P Preparata and Jean Vuillemin. “The cube-connected cycles: a versatile network for parallel computation”. In: Communications of the ACM 24.5 (1981), pp. 300–309.

[90] Prabhakar Raghavan and Eli Upfal. “Efficient routing in all-optical networks”. In: Proceedings of the twenty-sixth annual ACM symposium on Theory of computing. 1994, pp. 134–143.

[91] Justin Rattner. “The new age of supercomputing”. In: European Conference on Distributed Memory Computing. Springer. 1991, pp. 1–6.

[92] R Ravi. “Rapid rumor ramification: Approximating the minimum broadcast time”. In: Proceedings 35th Annual Symposium on Foundations of Computer Science. IEEE. 1994, pp. 202–213.

[93] R Reischuk. “An Algebraic Divide and Conquer Approach to Design Highly Parallel Solution Strategies for Optimization Problems on Graphs”. In: Technical Report. TH Darmstadt, 1991.

[94] Youcef Saad and Martin H Schultz. “Topological properties of hypercubes”. In: IEEE Transactions on computers 37.7 (1988), pp. 867–872.

[95] Peter Scheuermann and Geoffrey Wu. “Heuristic algorithms for broadcasting in point-to-point computer networks”. In: IEEE Computer Architecture Letters 33.09 (1984), pp. 804–811.

[96] Christian Schindelhauer. “On the inapproximability of broadcasting time”. In: International Workshop on Approximation Algorithms for Combinatorial Optimization. Springer. 2000, pp. 226–237.

[97] Steve R Seidel. “Circuit-switched vs. store-and-forward solutions to symmetric communication problems”. In: Proceedings of the 4th Conference on Hypercube Computers and Concurrent Applications. 1989, pp. 253–255.

[98] Steven R Seidel, Ming-Homg Lee, and Shivi Fotedar. “Concurrent bidirectional communication on the Intel iPSC/860 and iPSC/2”. In: The Sixth Distributed Memory Computing Conference, 1991. Proceedings. IEEE Computer Society. 1991, pp. 283–284.

[99] Charles L Seitz. “The cosmic cube”. In: Communications of the ACM 28.1 (1985), pp. 22–33.

[100] Peter J. Slater, Ernest J. Cockayne, and Stephen T. Hedetniemi. “Information dis- semination in trees”. In: SIAM Journal on Computing 10.4 (1981), pp. 692–701.

[101] Elena Stöhr. “Broadcasting in the butterfly network”. In: Information Processing Letters 39.1 (1991), pp. 41–43.

[102] Elena Stöhr. “On the broadcast time of the butterfly network”. In: International Workshop on Graph-Theoretic Concepts in Computer Science. Springer. 1991, pp. 226– 229.

[103] Abderezak Touzene and Brigitte Plateau. “Optimal multinode broadcast on a mesh connected graph with reduced bufferization”. In: European Conference on Distributed Memory Computing. Springer. 1991, pp. 143–152.

[104] Jonathan S Turner and Leonard F Wyatt. “A packet network architecture for integrated services”. In: Proceedings of GLOBECOM. Vol. 83. 1983, pp. 11–83.

[105] Frances Van Scoy. “Broadcasting a small number of messages in a square grid graph”. In: Proc. Seventeenth Allerton Conf. on Communication, Control and Computing. 1979.

[106] Emmanouel A Varvarigos and Dimitri P Bertsekas. “Communication algorithms for isotropic tasks in hypercubes and wraparound meshes”. In: Parallel Computing 18.11 (1992), pp. 1233–1257.

[107] Wikipedia. Cartesian product of graphs. URL: https : / / en . wikipedia . org/wiki/Cartesian_product_of_graphs.

[108] Wikipedia. Torus interconnect. URL: https://en.wikipedia.org/wiki/ Torus_interconnect#cite_note-1.

[109] Ouri Wolfson and Adrian Segall. “The communication complexity of atomic commitment and of gossiping”. In: SIAM Journal on Computing 20.3 (1991), pp. 423– 450.

[110] Jian-guo Zhou and Ke-min Zhang. “A minimum broadcast graph on 26 vertices”. In: Applied mathematics letters 14.8 (2001), pp. 1023–1026.