Answer:
This strategy of controlling one small island after another is called 'Island Hopping'
Explanation:
The idea is to muster all your forces and capture a small Island. Use this place as a base and as more reinforcements arrive, capture next Island. It is usually seen as a slow and expensive process.
However, it was successful executed by the Japanese as they expanded their reach across the South China Sea and the Pacific Ocean.
Similarly, the Allies and more importantly, the United States was also able to use it very successfully after the attack of Pearl harbor. The US Navy practiced island hopping eventually reaching close to Japanese shores, making it possible to launch devastating aerial attacks.
