On min-max cycle bases

被引:0
|
作者
Galbiati, G [1 ]
机构
[1] Univ Pavia, Dipartimento Informat & Sistemist, I-27100 Pavia, Italy
来源
关键词
D O I
暂无
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
An undirected biconnected graph G with non negative weights on the edges is given. In the cycle space associated with G, a subspace of the vector space of G, we define as weight of a basis the maximum among the weights of the cycles of the basis. The problem we consider is that of finding a basis of minimum weight for the cycle space. It is easy to see that if we do not put additional constraints on the basis, then the problem is easy and there are fast algorithms for solving it. On the other hand if we require the basis to be fundamental, i.e. to consist of the set of all fundamental cycles of G with respect to the chords of a spanning tree of G, then we show that the problem is NP-hard and cannot be approximated within 2 - is an element of,For Allis an element of > 0, even with uniform weights, unless P=NP. We also show that the problem remains NP-hard when restricted to the class of complete graphs; in this case it cannot be approximated within 13/11 - is an element of,For Allis an element of > 0, unless P=NP; it is instead approximable within 2 in general, and within 3/2 if the triangle inequality holds.
引用
收藏
页码:116 / 123
页数:8
相关论文
共 50 条
  • [31] Dynamic min-max problems
    Schwiegelshohn, U
    Thiele, L
    [J]. DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS, 1999, 9 (02): : 111 - 134
  • [32] Analysis of min-max systems
    Olsder, GJ
    [J]. RAIRO-RECHERCHE OPERATIONNELLE-OPERATIONS RESEARCH, 1996, 30 (01): : 17 - 30
  • [33] BOUNDS FOR MIN-MAX HEAPS
    HASHAM, A
    SACK, JR
    [J]. BIT, 1987, 27 (03): : 315 - 323
  • [34] On a min-max theorem of cacti
    Szigeti, Z
    [J]. INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION, 1998, 1412 : 84 - 95
  • [35] Max-max, max-min, min-max and min-min knapsack problems with a parametric constraint
    Halman, Nir
    Kovalyov, Mikhail Y.
    Quilliot, Alain
    [J]. 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH, 2023, 21 (02): : 235 - 246
  • [36] On stabilization of min-max systems
    Zhao, QC
    Zheng, DZ
    [J]. AUTOMATICA, 2003, 39 (04) : 751 - 756
  • [37] Reflected min-max heaps
    Makris, C
    Tsakalidis, A
    Tsichlas, K
    [J]. INFORMATION PROCESSING LETTERS, 2003, 86 (04) : 209 - 214
  • [38] AN EXTENSION OF MIN-MAX THEOREM
    PONSTEIN, J
    [J]. SIAM REVIEW, 1965, 7 (02) : 181 - &
  • [39] MIN-MAX FOR MULTIPLE CRITERIA
    DRAGUSIN, C
    [J]. RAIRO-RECHERCHE OPERATIONNELLE-OPERATIONS RESEARCH, 1978, 12 (02): : 169 - 180
  • [40] Dynamic Min-Max Problems
    Uwe Schwiegelshohn
    Lothar Thiele
    [J]. Discrete Event Dynamic Systems, 1999, 9 : 111 - 134