Interesting question. At a given temperature, say 32 degrees Fahrenheit, the material that makes ice melt the fastest is the material that lowers the freezing point of water the most. Pure water has a freezing point at 32 degrees Fahrenheit, below which it behaves as a solid and above which it behaves as a liquid.

Temperature is an indication of how fast particles such as molecules, atoms, and ions are vibration. When liquid water is in contact with ice at the freezing temperature, liquid water molecules are vibrating slow enough to be captured on the surface of the ice. At the same time, molecules on the surface of the ice are vibrating fast enough to escape into the liquid, but not so fast as to outpace the number of molecules being captured on the surface of the ice. The rate of capture and escape is the same, and so the ice will remain as ice and the liquid water will remain as liquid water. If the temperature decreases below the freezing point, the water molecules are vibrating slow enough that the number of captures is greater than the number of escapes, and all of the water freezes.

To lower the freezing point of water, all you have to do is add particles! It could be almost anything that forms a solution (a uniform mixture) with liquid water. Table salt or sugar could do the trick. Salts are the most common molecular compounds used to lower the freezing point of water. Salts are neutral and bound positive and negative ions. Table salt, for example, consists of a sodium ion Na+ bonded to a chlorine ion Cl-. When mixed with water, salts dissociate into their constituent ions. A mixture of water and table salt is really a mixture of H₂O molecules, Na+ ions, and Cl- ions.

Adding particles like salt ions to liquid water and ice creates a uniform solution of liquid water and the ions. However, the particles don't form a solution in the ice; ice is pure water. Because the concentration of water in the solution is lower than the concentration of water in pure ice, the rate of water capture on the surface of the ice decreases, and the rate of escape of water from the ice of the ice increases. We see this as a decrease in the freezing point of water.

The more particles you can dissolve in the liquid water, the more you decrease its freezing point. Consequently, a mixture of 20% NaCl and liquid water will have a lower freezing point (2 degrees Fahrenheit) than a mixture of 10% NaCl and liquid water (20 degrees Fahrenheit). The 20% solution will thus melt ice faster (though it isn't practical).

If you were to use a salt that dissociates into a greater number of ions, you would lower the temperature even further. Calcium chloride, CaCl₂, dissociates into 3 ions, one Ca₂⁺ ion and two Cl- ions. The lowest freezing point of a practical CaCl₂:H₂O solution is -20 degrees Fahrenheit, compared to 15 degrees Fahrenheit, the lowest freezing point of a practical NaCl:H₂O solution.

The material that melts ice the fastest is the material that dissociates into the greatest number of particles in a solution of that material and liquid water.