I made a post about this in r/hyderabad. I thought I might as well post it here too.

Killing stray dogs or capturing them and putting them in shelters won't eradicate the problem.

1. It is simply impossible to kill/capture every single stray dog in India. Hypothetically if you managed to kill/capture 80% of the dogs, you will be eliminating competition for the remaining 20% of the stray dogs. They will eat all the garbage they can find on streets and reproduce violently. Eventually you will have a situation where the number of dogs outside will be equal to the number of dogs inside/killed.
2. Hypothetically you managed to kill/capture 100% of all the dogs in a city then dogs from the neighboring city/town/village will move in and settle in that city. As there is no competition for resources, they will thrive & reproduce violently.
3. Hypothetically you manage to kill/capture 100% of all the dogs in every city/town/village simultaneously it still won't solve the problem because pets are routinely abandoned on the street. Those pets will thrive on the garbage left in the street and reproduce violently.
4. Killing dogs is not only a cruel solution, their bodies will decompose and release greenhouse gasses which is bad for our environment. A better solution is to ensure dogs are not born in the first place then to eliminate them.

The only practical, long lasting solution to the stray dog problem is to cut their food. Stop feeding them, stop throwing garbage in the street. This is a very very humane solution not only for them, but also for us humans too.