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J. Hyam Rubinstein

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Works connected to Doreen A. Thomas

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J. H. Ru­bin­stein and D. Thomas: The Stein­er prob­lem of shortest net­works, 1988. From un­pub­lished pro­ceed­ings of the third Aus­trali­an tele­traffic re­search sem­in­ar (Mel­bourne, Novem­ber 1988). misc

J. H. Ru­bin­stein and D. Thomas: Min­im­al cost net­works in the plane, 1989. From un­pub­lished pro­ceed­ings of the fourth Aus­trali­an tele­traffic re­search sem­in­ar (Bond Uni­versity, Ro­bina, Aus­tralia, Decem­ber 1989). misc

J. H. Ru­bin­stein and D. A. Thomas: “A vari­ation­al ap­proach to the Stein­er net­work prob­lem,” Ann. Op­er. Res. 33 : 6 (1991), pp. 481–​499. MR 1140992 Zbl 0734.​05040 article

J. H. Ru­bin­stein and D. A. Thomas: “The Stein­er ra­tio con­jec­ture for six points,” J. Comb. The­ory, Ser. A 58 : 1 (September 1991), pp. 54–​77. MR 1119701 Zbl 0739.​05034 article

J. H. Ru­bin­stein, D. A. Thomas, and J. F. Weng: “De­gree-five Stein­er points can­not re­duce net­work costs for planar sets,” Net­works 22 : 6 (1992), pp. 531–​537. MR 1178862 Zbl 0774.​05032 article

J. H. Ru­bin­stein and D. A. Thomas: “The Stein­er ra­tio con­jec­ture for co­cir­cu­lar points,” Dis­crete Com­put. Geom. 7 : 1 (1992), pp. 77–​86. MR 1134454 Zbl 0774.​05031 article

J. H. Ru­bin­stein and D. A. Thomas: “Gra­ham’s prob­lem on shortest net­works for points on a circle,” pp. 193–​218 in The Stein­er prob­lem, published as Al­gorith­mica 7 : 2–​3. Issue edi­ted by F. K. Hwang. 1992. MR 1146495 Zbl 0748.​05051 incollection

J. H. Ru­bin­stein, D. Thomas, and N. Wormald: Al­gorithms for con­strained net­works, 1992. From un­pub­lished pro­ceed­ings of the sev­enth Aus­trali­an tele­traffic re­search sem­in­ar (Man­num, Aus­tralia, Novem­ber 1992). misc

D. A. Thomas, J. H. Ru­bin­stein, and T. Cole: “The Stein­er min­im­al net­work for con­vex con­fig­ur­a­tions,” Dis­crete Com­put. Geom. 9 : 3 (1993), pp. 323–​333. MR 1204786 Zbl 0774.​05033 article

M. Brazil, T. Cole, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Min­im­al Stein­er trees for \( 2^k\times 2^k \) square lat­tices,” J. Comb. The­ory, Ser. A 73 : 1 (1996), pp. 91–​110. MR 1367609 Zbl 0844.​05036 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Full min­im­al Stein­er trees on lat­tice sets,” J. Com­bin. The­ory Ser. A 78 : 1 (April 1997), pp. 51–​91. MR 1439632 Zbl 0874.​05018 article

J. H. Ru­bin­stein, D. A. Thomas, and N. C. Wormald: “Stein­er trees for ter­min­als con­strained to curves,” SIAM J. Dis­crete Math. 10 : 1 (1997), pp. 1–​17. MR 1430542 Zbl 0869.​05023 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Min­im­al Stein­er trees for rect­an­gu­lar ar­rays of lat­tice points,” J. Comb. The­ory, Ser. A 79 : 2 (August 1997), pp. 181–​208. MR 1462554 Zbl 0883.​05038 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Shortest net­works on spheres,” pp. 453–​461 in Net­work design: Con­nectiv­ity and fa­cil­it­ies loc­a­tion (Prin­ceton, NJ, 28–30 April 1997). Edi­ted by P. M. Pardalos and D.-Z. Du. DIMACS Series in Dis­crete Math­em­at­ics and The­or­et­ic­al Com­puter Sci­ence 40. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1998. MR 1613017 Zbl 0915.​05043 incollection

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, and J. F. Weng: Mod­el­ling and op­tim­isa­tion of a weighted net­work in an un­der­ground mine design, 2001. From un­pub­lished pro­ceed­ings of the third in­ter­na­tion­al con­fer­ence on con­trol the­ory and ap­plic­a­tions (Pre­tor­ia, South Africa, 12–14 Decem­ber 2001). misc

J. H. Ru­bin­stein, D. A. Thomas, and N. C. Wormald: “A poly­no­mi­al al­gorithm for a con­strained trav­el­ing sales­man prob­lem,” Net­works 38 : 2 (September 2001), pp. 68–​75. MR 1852365 Zbl 0990.​90102 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Gradi­ent-con­strained min­im­um net­works, I: Fun­da­ment­als,” J. Glob. Op­tim. 21 : 2 (2001), pp. 139–​155. Part III was pub­lished in J. Op­tim. The­ory Ap­pl. 155:1 (2012). Ru­bin­stein was not a co-au­thor of part II. MR 1863330 Zbl 1068.​90605 article

J. H. Ru­bin­stein, D. A. Thomas, and J. Weng: “Min­im­um net­works for four points in space,” Geom. Ded­icata 93 : 1 (2002), pp. 57–​70. MR 1934686 Zbl 1009.​05042 article

M. Brazil, D. Lee, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “A net­work mod­el to op­tim­ise cost in un­der­ground mine design,” Trans. S. Afr. Inst. Elec­tr. Eng. 93 : 2 (2002), pp. 97–​103. article

M. Brazil, D. Lee, M. Van Leuven, J. H. Ru­bin­stein, D. A. Thomas, and N. C. Wormald: “Op­tim­ising de­clines in un­der­ground mines,” Min­ing Tech. 112 : 3 (2003), pp. 164–​170. article

M. Brazil, D. A. Thomas, J. F. Weng, J. H. Ru­bin­stein, and D. H. Lee: “Cost op­tim­isa­tion for un­der­ground min­ing net­works,” Op­tim. Eng. 6 : 2 (2005), pp. 241–​256. MR 2136609 Zbl 1093.​90067 article

M. Brazil, D. Lee, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. C. Wormald: “Op­tim­isa­tion in the design of un­der­ground mine ac­cess,” pp. 121–​124 in Orebody mod­el­ling and stra­tegic mine plan­ning: Un­cer­tainty and risk man­age­ment mod­els. Edi­ted by R. Di­mitrako­poulos. Spec­trum Series 14. Aus­tralasi­an In­sti­tute of Min­ing and Me­tal­lurgy (Mel­bourne), 2005. incollection

M. Brazil, P. A. Gross­man, D. H. Lee, J. H. Ru­bin­stein, D. A. Thomas, and N. C. Wormald: “De­cline design in un­der­ground mines us­ing con­strained path op­tim­isa­tion,” Min­ing Tech. 117 : 2 (2008), pp. 93–​99. article

M. Brazil, P. A. Gross­man, D. A. Thomas, J. H. Ru­bin­stein, D. Lee, and N. C. Wormald: “Con­strained path op­tim­isa­tion for un­der­ground mine lay­out,” pp. 856–​861 in Pro­ceed­ings of the World Con­gress on En­gin­eer­ing 2007 (Im­per­i­al Col­lege, Lon­don, 2–4 Ju­ly 2007), vol. II. Edi­ted by S. I. Ao, L. Gel­man, D. Hukins, A. Hunter, and A. M. Kor­sun­sky. Lec­ture Notes in En­gin­eer­ing and Com­puter Sci­ence 2166. News­wood Lim­ited (Hong Kong), 2008. incollection

A. J. Chang, M. Brazil, J. H. Ru­bin­stein, and D. A. Thomas: “Curvature-con­strained dir­ec­tion­al-cost paths in the plane,” J. Glob. Op­tim. 53 : 4 (2012), pp. 663–​681. MR 2944057 Zbl 06117793 article

M. Brazil, J. H. Ru­bin­stein, D. A. Thomas, J. F. Weng, and N. Wormald: “Gradi­ent-con­strained min­im­um net­works, III: Fixed to­po­logy,” J. Op­tim. The­ory Ap­pl. 155 : 1 (2012), pp. 336–​354. Part I was pub­lished in J. Glob. Op­tim. 21:2 (2001). Ru­bin­stein was not a co-au­thor of part II. MR 2983123 Zbl 1255.​90120 article