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A method for determining the highest available-bandwidth paths in a core-stateless network, with or without restrictions, is proposed. The method keeps track of the possible solution range as it progresses, can operate under number of hops, delay or cost constraints, and induces load balancing and high network resource utilization. The method is combined with a token-based transfer of information and semaphore mechanism to avoid over-allocation and ensure resource allocation coordination along the logical ring of the ingress nodes. The resulted connection admission control procedure alleviates the scalability problem by keeping all the admission control operations in the ingress nodes while preserving the guaranteed service semantics and providing a low-latency, quasi-parallel allocation under light load and a centralized/semaphored allocation under heavy load. The widest path search algorithm is illustrated and compared with other existing algorithms.