Conditional Inequalities and the Shortest Common Superstring Problem

We investigate the shortest common superstring problem (SCSSP). As SCSSP is APX-complete it cannot be approximated within an arbitrarily small performance ratio. One heuristic that is widely used is the notorious greedy heuristic. It is known, that the performance ratio of this heuristic is at least 2 and not worse than 4. It is conjectured that the greedy heuristic’s performance ratio is in fact 2 (the greedy conjecture). Even the best algorithms introduced for SCSSP can only guarantee an upper bound of 2.5. In [11] an even stronger version of the greedy conjecture is proven for a restricted class of orders in which strings are merged. We extend these results by broadening the class for which this stronger version can be established. We also show that the Triple inequality, introduced in [11] and crucial for their results, is inherently insufficient to carry the proof for the greedy conjecture in the general case. Finally we describe how linear programming can be used to support research along this line.