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ΠΠΏΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΠΎΠ½Π½Π°Ρ ΡΡ Π΅ΠΌΠ° Π₯Π°ΠΉΠΌΠΎΠ²ΠΈΡΠ° - Π ΠΈΠ½Π½ΠΎΡ ΠΠ°Π½Π° Π΄Π»Ρ CVRP Π² ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π°Ρ ΡΠΈΠΊΡΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΡΡΠΈ ΡΠ΄Π²ΠΎΠ΅Π½ΠΈΡ
The Capacitated Vehicle Routing Problem (CVRP) is a classical extremal combinatorial routing problem with numerous applications in operations research. Although the CVRP is strongly NP-hard both in the general case and in the Euclidean plane, it admits quasipolynomial- and even polynomial-time approximation schemes (QPTAS and PTAS) in Euclidean spaces of fixed dimension. At the same time, the metric setting of the problem is APX-complete even for an arbitrary fixed capacity q β₯ 3. In this paper, we show that the classical Haimovich-Rinnooy Kan algorithm implements a PTAS and an Efficient Polynomial-Time Approximation Scheme (EPTAS) in an arbitrary metric space of fixed doubling dimension for q = o(log log n) and for an arbitrary constant capacity, respectively. Β© 2019 Krasovskii Institute of Mathematics and Mechanics. All right reserved