From the beginning of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. Among the authors of early sorting algorithms around 1951 was Betty Holberton (born Snyder), who worked on ENIAC and UNIVAC. Bubble sort was analyzed as early as 1956. Comparison sorting algorithms have a fundamental requirement of Ω("n" log "n") comparisons (some input sequences will require a multiple of "n" log "n" comparisons, where n is the number of elements in the array to be sorted). Algorithms not based on comparisons, such as counting sort, can have better performance. Asymptotically optimal algorithms have been known since the mid-20th century—useful new algorithms are still being invented, with the now widely used Timsort dating to 2002, and the library sort being first published in 2006.