1. A distributed resource scheduling system for a plurality of hosts, comprising: a root scheduler configured to: issue a constrained placement request to distributed scheduler software components in one or more 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 of the virtual computing instance is to be satisfied based on a comparison of responses received from the branch schedulers, 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: forward the constrained placement request issued by the root scheduler to one or more of the hosts associated with the branch scheduler and satisfying the placement constraints of the request, compare responses from the one or more 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 in response to receipt of the constrained placement request, issue a response indicative of the available resources for the constrained placement request to a parent branch scheduler.