Doze

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Doze is a nifty small application that prevents apps installed on your phone or tablet from sending or receiving data through your Internet network. Read more about Doze  

In order to work, Doze needs to setup a VPN connection on your phone. When the device’s screen is off, the app automatically prevents other applications installed on your device from sending or receiving data, but it doesn’t disable your Wi-Fi or mobile data connection.
 
The app can potentially add more hours to standby time and can improve your battery’s life. Apps do resume their activity when you turn the screen on to check for messages or notifications. It also lets you create a list of apps that you would like to run in the background and check for notifications. The app comes with an aggressive mode which makes Doze active whether the screen is on or off and only when you open a certain app, can it access the network.