Stable Marriage Problem With Ties and Incomplete Bounded Length Preference List Under Social Stability

Abstract

We consider a variant of socially stable marriage problem where preference lists may be incomplete, may contain ties and may have bounded length. In real world application like NRMP and Scottish medical matching scheme such restrictions arise very frequently where set of agents (man/woman) is very large and providing a complete and strict order preference list is practically in-feasible. In presence of ties in preference lists, the most common solution is weakly socially stable matching. It is a fact that in an instance, weakly stable matching can have different sizes. This motivates the problem of finding a maximum cardinality weakly socially stable matching. In this paper, we find maximum size weakly socially stable matching for an instance of Stable Marriage problem with Ties and Incomplete bounded length preference list with Social Stability. The motivation to consider this instance is the known fact, any larger instance of this problem is NP-hard.

Energy efficient and fair resource allocation for LTE‐unlicensed uplink networks: A two‐sided matching approach with partial information

“…As proven in the aforementioned statement, stability and Pareto optimality have been guaranteed by using Algorithm 1, meaning that there are no incentives for any CUs and UBs to form new matching. However, the preference lists of CUs could be incomplete; some CUs may be unmatched …”

“…However, the preference lists of CUs could be incomplete; some CUs may be unmatched. 38,39 To further maximize system's EE by increasing the number of CUs matched by Algorithm 2, an iteration of Algorithm 2 begins with an unmatched CU k proposing to its most favorite UB u , and UB u would be deleted from the preference list of CU k . An SCBS would consider this proposal acceptable if the following criteria are fulfilled.…”