Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Approximation algorithm for the Min-Max partial tree cover problem. |
| Συγγραφείς: |
Zhao, Lei1 (AUTHOR) zhaolei@zjnu.edu.cn, Zhang, Zhao1 (AUTHOR) hxhzz@sina.com |
| Πηγή: |
Mathematical Methods of Operations Research. Jun2026, Vol. 103 Issue 1/2, p299-310. 12p. |
| Θεματικοί όροι: |
*Algorithms, *Mathematical optimization, Approximation algorithms, Weighted graphs, Graph theory |
| Περίληψη: |
This paper investigates the Min-Max Partial Tree Cover (MinMaxPTC) problem. Given an edge-weighted graph G = (V , E) , an integer k and a real number q ∈ R + , each vertex is associated with a non-negative profit, the MinMaxPTC problem asks for k trees to collect profit at least q (that is, the total profit of those vertices covered by these trees is no less than q) such that the weight of a heaviest tree is minimized. In its rooted version, the Rooted Min-Max Partial Tree Cover (R-MinMaxPTC) problem, every tree is required to contain a prescribed vertex (called root). For MinMaxPTC, we propose a (1 - e - α , 1 + ε) -bicriteria approximation algorithm, which computes k trees collecting profit at least α q such that the weight of a heaviest tree computed by the algorithm does not exceed 1 + ε times the optimal weight, where α is the approximation ratio for the Budgeted Tree Cover (BTC) problem. The algorithm can be generalized to deal with the R-MinMaxPTC problem, yielding an (α ′ 1 + α ′ , 1 + ε) -bicriteria approximation, where α ′ is the approximation ratio for the rooted BTC problem. We also present an (1 + ε) · ⌈ log 1 + α ′ q ⌉ + 1 -approximation algorithm for R-MinMaxPTC without violating feasibility. [ABSTRACT FROM AUTHOR] |
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