The study of optimal algorithms for solving given practical problems is closely associated with the term "green computing". Efficient algorithm can solve a given problem in a reasonable time, reducing the energy consumptions by computer. Let us recall, for example, that optimal sorting algorithms (like "merge sort") run in \( O(n \log(n)) \) time, while the naive algorithms (like "insertion sort") works in \( O(n^2) \) time. For large array, say of order \( 10^7 \), and in typical situations and on quite fast computer the merge sort algorithm will finish its work after a few seconds, while the insertion sort will require several hours for the same job. So, the application of proper algorithm has a crucial impact on energy saving during computation.

In many cases a reasonable heuristics can quickly find an approximated solution of a complicated optimization problems which a acceptable from a practical point of view.

The problem of energy efficient computing is specially important in wireless environment, where the computing devices waste a lot of energy for wireless communication and specially when their sources of energy are batteries. Important examples of such systems are sensors fields monitoring environment - in this situation frequent replacement of the battery can be very expensive.

This is of course not a precise description of the problem. We must specify additional properties of our devices - for example we will assume each two devices may listen each other radio signals (such a network is called a "single-hop" network). In the following discussion we will also assume that a time is divided in a short time-slots. We will also assume that each device, when listening to the common radio channel, can distinguish whether nobody else sends a signal or some other device or devices send a signal.

In the following sections we will discuss the most efficient algorithms for leader election known at the end of the year 2014. We will show that this algorithms are very efficient from energetic point of view.