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Volumn , Issue , 2014, Pages 424-433

Pat/h finding methods for linear programming: Solving linear programs in õ(rank) iterations and faster algorithms for maximum flow

Author keywords

Interior point; linear program; maximum flow

Indexed keywords

FLOW GRAPHS; ITERATIVE METHODS; LINEAR SYSTEMS; POLYNOMIAL APPROXIMATION;

EID: 84920044028     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2014.52     Document Type: Conference Paper
Times cited : (389)

References (47)
  • 2
    • 0039662580 scopus 로고    scopus 로고
    • Volumetric path following algorithms for linear programming
    • Kurt M. Anstreicher. Volumetric path following algorithms for linear programming. Math. Program., 76:245-263, 1996.
    • (1996) Math. Program. , vol.76 , pp. 245-263
    • Anstreicher, K.M.1
  • 6
    • 0015330635 scopus 로고
    • Theoretical improvements in algorithmic efficiency for network flow problems
    • Jack Edmonds and Richard M Karp. Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM (JACM), 19(2):248-264, 1972.
    • (1972) Journal of the ACM (JACM) , vol.19 , Issue.2 , pp. 248-264
    • Edmonds, J.1    Karp, R.M.2
  • 7
    • 0000682065 scopus 로고
    • Network flow and testing graph connectivity
    • Shimon Even and R Endre Tarjan. Network flow and testing graph connectivity. SIAM journal on computing, 4(4):507-518, 1975.
    • (1975) SIAM Journal on Computing , vol.4 , Issue.4 , pp. 507-518
    • Even, S.1    Endre Tarjan, R.2
  • 9
    • 2342592299 scopus 로고
    • Barrier functions and interior-point algorithms for linear programming with zero-, one-, or two-sided bounds on the variables
    • Robert M Freund and Michael J Todd. Barrier functions and interior-point algorithms for linear programming with zero-, one-, or two-sided bounds on the variables. Mathematics of Operations Research, 20(2):415-440, 1995.
    • (1995) Mathematics of Operations Research , vol.20 , Issue.2 , pp. 415-440
    • Freund, R.M.1    Todd, M.J.2
  • 10
    • 0023997284 scopus 로고
    • An o (n 2 (m+ n log n) log n) mincost flow algorithm
    • Zvi Galil and va Tardos. An o (n 2 (m+ n log n) log n) mincost flow algorithm. Journal of the ACM (JACM), 35(2):374-386, 1988.
    • (1988) Journal of the ACM (JACM) , vol.35 , Issue.2 , pp. 374-386
    • Galil, Z.1    Tardos, V.2
  • 11
    • 0032157143 scopus 로고    scopus 로고
    • Beyond the flow decomposition barrier
    • Andrew V. Goldberg and Satish Rao. Beyond the flow decomposition barrier. J. ACM, 45(5):783-797, 1998.
    • (1998) J. ACM , vol.45 , Issue.5 , pp. 783-797
    • Goldberg, A.V.1    Rao, S.2
  • 12
    • 0001764412 scopus 로고
    • Finding minimumcost circulations by successive approximation
    • Andrew V Goldberg and Robert E Tarjan. Finding minimumcost circulations by successive approximation. Mathematics of Operations Research, 15(3):430-466, 1990.
    • (1990) Mathematics of Operations Research , vol.15 , Issue.3 , pp. 430-466
    • Goldberg, A.V.1    Tarjan, R.E.2
  • 13
    • 0026876871 scopus 로고
    • Path-following methods for linear programming
    • Clovis C Gonzaga. Path-following methods for linear programming. SIAM review, 34(2):167-224, 1992.
    • (1992) SIAM Review , vol.34 , Issue.2 , pp. 167-224
    • Clovis, C.1    Gonzaga2
  • 15
    • 0032267769 scopus 로고    scopus 로고
    • Better random sampling algorithms for flows in undirected graphs
    • Society for Industrial and Applied Mathematics
    • David R Karger. Better random sampling algorithms for flows in undirected graphs. In Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms, pages 490-499. Society for Industrial and Applied Mathematics, 1998.
    • (1998) Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms , pp. 490-499
    • Karger, D.R.1
  • 18
    • 0030134435 scopus 로고    scopus 로고
    • Rounding of polytopes in the real number model of computation
    • Leonid G Khachiyan. Rounding of polytopes in the real number model of computation. Mathematics of Operations Research, 21(2):307-320, 1996.
    • (1996) Mathematics of Operations Research , vol.21 , Issue.2 , pp. 307-320
    • Khachiyan, L.G.1
  • 23
    • 32844462374 scopus 로고    scopus 로고
    • Simulated annealing in convex bodies and an o∗(n4) volume algorithm
    • L zl Lov z and Santosh Vempala. Simulated annealing in convex bodies and an o∗(n4) volume algorithm. J. Comput. Syst. Sci., 72(2):392-417, 2006.
    • (2006) J. Comput. Syst. Sci. , vol.72 , Issue.2 , pp. 392-417
    • Lovz, L.1    Vempala, S.2
  • 24
    • 78751561518 scopus 로고    scopus 로고
    • Fast approximation algorithms for cutbased problems in undirected graphs
    • Aleksander Madry. Fast approximation algorithms for cutbased problems in undirected graphs. In FOCS, pages 245-254, 2010.
    • (2010) FOCS , pp. 245-254
    • Madry, A.1
  • 26
  • 28
    • 37549070373 scopus 로고    scopus 로고
    • Rounding of convex sets and efficient gradient methods for linear programming problems
    • February
    • Yu. Nesterov. Rounding of convex sets and efficient gradient methods for linear programming problems. Optimization Methods Software, 23(1):109-128, February 2008.
    • (2008) Optimization Methods Software , vol.23 , Issue.1 , pp. 109-128
    • Nesterov, Y.1
  • 29
    • 0031073753 scopus 로고    scopus 로고
    • Self-scaled barriers and interior-point methods for convex programming
    • Yu E Nesterov and Michael J Todd. Self-scaled barriers and interior-point methods for convex programming. Mathematics of Operations research, 22(1):1-42, 1997.
    • (1997) Mathematics of Operations Research , vol.22 , Issue.1 , pp. 1-42
    • Nesterov, Y.E.1    Todd, M.J.2
  • 32
    • 0027554501 scopus 로고
    • A faster strongly polynomial minimum cost flow algorithm
    • James B Orlin. A faster strongly polynomial minimum cost flow algorithm. Operations research, 41(2):338-350, 1993.
    • (1993) Operations Research , vol.41 , Issue.2 , pp. 338-350
    • Orlin, J.B.1
  • 35
    • 0023862337 scopus 로고
    • A polynomial-time algorithm, based on newton's method, for linear programming
    • James Renegar. A polynomial-time algorithm, based on newton's method, for linear programming. Mathematical Programming, 40(1-3):59-93, 1988.
    • (1988) Mathematical Programming , vol.40 , Issue.1-3 , pp. 59-93
    • Renegar, J.1
  • 37
    • 57049148610 scopus 로고    scopus 로고
    • Graph sparsification by effective resistances
    • Daniel A. Spielman and Nikhil Srivastava. Graph sparsification by effective resistances. In STOC, pages 563-568, 2008.
    • (2008) STOC , pp. 563-568
    • Spielman, D.A.1    Srivastava, N.2
  • 40
    • 51249170715 scopus 로고
    • A strongly polynomial minimum cost circulation algorithm
    • va Tardos. A strongly polynomial minimum cost circulation algorithm. Combinatorica, 5(3):247-255, 1985.
    • (1985) Combinatorica , vol.5 , Issue.3 , pp. 247-255
    • Tardos, V.1
  • 41
    • 0023604331 scopus 로고
    • An algorithm for linear programming which requires o(((m + n)n2 + (m + n)1.5n)l) arithmetic operations
    • Pravin M. Vaidya. An algorithm for linear programming which requires o(((m + n)n2 + (m + n)1.5n)l) arithmetic operations. In STOC, pages 29-38, 1987.
    • (1987) STOC , pp. 29-38
    • Vaidya, P.M.1
  • 42
    • 0024769505 scopus 로고
    • A new algorithm for minimizing convex functions over convex sets (extended abstract)
    • Pravin M. Vaidya. A new algorithm for minimizing convex functions over convex sets (extended abstract). In FOCS, pages 338-343, 1989.
    • (1989) FOCS , pp. 338-343
    • Vaidya, P.M.1
  • 44
    • 0025558397 scopus 로고
    • Reducing the parallel complexity of certain linear programming problems (extended abstract)
    • Pravin M. Vaidya. Reducing the parallel complexity of certain linear programming problems (extended abstract). In FOCS, pages 583-589, 1990.
    • (1990) FOCS , pp. 583-589
    • Vaidya, P.M.1
  • 45
    • 0001536423 scopus 로고    scopus 로고
    • A new algorithm for minimizing convex functions over convex sets
    • Pravin M Vaidya. A new algorithm for minimizing convex functions over convex sets. Mathematical Programming, 73(3):291-341, 1996.
    • (1996) Mathematical Programming , vol.73 , Issue.3 , pp. 291-341
    • Vaidya, P.M.1
  • 46
    • 0042216503 scopus 로고
    • A technique for bounding the number of iterations in path following algorithms
    • Pravin M Vaidya and David S Atkinson. A technique for bounding the number of iterations in path following algorithms. Complexity in Numerical Optimization, pages 462-489, 1993.
    • (1993) Complexity in Numerical Optimization , pp. 462-489
    • Vaidya, P.M.1    Atkinson, D.S.2
  • 47
    • 84862595166 scopus 로고    scopus 로고
    • Multiplying matrices faster than coppersmith-winograd
    • Virginia Vassilevska Williams. Multiplying matrices faster than coppersmith-winograd. In STOC, pages 887-898, 2012.
    • (2012) STOC , pp. 887-898
    • Williams, V.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.