1. A distributed resource scheduling system for a plurality of hosts, comprising: a root scheduler configured to: issue a constrained placement request for placing a virtual computing instance to distributed scheduler software components in a randomly chosen subset of branch schedulers associated with hosts satisfying placement constraints of the request and receive responses thereto, select one of the hosts by which the constrained placement request is to be satisfied based on a comparison of responses received from the branch schedulers to which the constrained placement request is issued, and cause the virtual computing instance to be executed on the selected host; a plurality of branch schedulers, each associated with the root scheduler and a distinct set of the hosts and configured with a distributed scheduler software component configured to, responsive to receiving the constrained placement request issued by the root scheduler: forward the constrained placement request to a randomly chosen subset of the hosts associated with the branch scheduler and satisfying the placement constraints of the request and receive responses thereto, compare the responses from the hosts to which the constrained placement request is forwarded, and forward the response of one of the hosts to the root scheduler, based on the comparison; and a plurality of hosts, each configured with a distributed scheduler software component configured to: maintain data representative of available resources therein, and responsive to receipt of the constrained placement request, issue a response indicative of available resources for the constrained placement request to a parent branch scheduler.