Papers › Rankability and Linear Ordering Problem: New Probabilistic Insight and Algorithms
Rankability and Linear Ordering Problem: New Probabilistic Insight and Algorithms
Leszek Szczecinski, Harsh Sukheja
The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether the data are rankable, that is, if the linear ordering problem (LOP) solutions have a meaningful interpretation, received much less attention. To address this problem, we adopt a probabilistic perspective where the results of pairwise comparisons are modeled as Bernoulli variables with a common parameter and we estimate the latter from the observed data. The brute-force approach to the required enumeration has a prohibitive complexity of O(M !), so we reformulate the problem and introduce a concept of the Slater spectrum that generalizes the Slater index, and then devise an algorithm to find the spectrum with complexity O(M^3 2^M) that is manageable for moderate values of M. Furthermore, with a minor modification of the algorithm, we are able to find all solutions of the LOP with the complexity O(M 2^M). Numerical examples are shown on synthetic and real-world data, and the algorithms are publicly available.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections