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Decomposition algorithms for minimal cut problems

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  • Suleyman Tufekci

Abstract

Consider a network G(N. A) with n nodes, where node 1 designates its source node and node n designates its sink node. The cuts (Zi, =), i= 1…, n ‐ 1 are called one‐node cuts if 1 ϵ Zi,. n q Zi, Z1‐− {1}, Zi ϵ Zi+1 and Zi and Zi+l differ by only one node. It is shown that these one‐node cuts decompose G into 1 m n/2 subnetworks with known minimal cuts. Under certain circumstances, the proposed one‐node decomposition can produce a minimal cut for G in 0(n2 ) machine operations. It is also shown that, under certain conditions, one‐node cuts produce no decomposition. An alternative procedure is also introduced to overcome this situation. It is shown that this alternative procedure has the computational complexity of 0(n3).

Suggested Citation

  • Suleyman Tufekci, 1981. "Decomposition algorithms for minimal cut problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(3), pages 431-445, September.
    • Handle: RePEc:wly:navlog:v:28:y:1981:i:3:p:431-445
    DOI: 10.1002/nav.3800280308
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