On Computing Janet Bases for Degree Compatible Orderings
  We consider three modifications of our involutive algorithm for computing Janet bases. These modifications are related to degree compatible monomial orders and specify selection strategies for non-multiplicative prolongations. By using the standard data base of polynomial benchmarks for \Gr bases software we compare the modifications and confront them with Magma that implements Faug\`{e}re's $F_4$ algorithm. 
Vladimir P. Gerdt, Yuri A.Blinkov