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2 | Problem Class | Name | Supports Ties | Supports MultiInstance | Supports Incomplete Lists | Supports One2Many | Supports Odd #Roommates | Description | Reference | ||||||||||||||||||||||
3 | SR | Tan-Hsueh | Y | N | Y | N | Y | Produces a reduced stable partition in a given instance (arbitrary tie break). | https://doi.org/10.1016/0166-218X(93)E0154-Q | ||||||||||||||||||||||
4 | SR | No-Ties Stable | N | Y | Y | N | Y | Produces a stable matching or reports that none exists. | https://doi.org/10.1016/0196-6774(85)90033-1 | ||||||||||||||||||||||
5 | SR | Maximum Stable | N | N | Y | N | Y | Produces a maximum stable matching by deleting one agent from each odd cycle of a reduced stable partition. | https://doi.org/10.1080/00207169108803975 | ||||||||||||||||||||||
6 | SR | All Stable Matchings | N | N | Y | N | N | Finds all (if any) admitted stable matchings through enumeration. | https://doi.org/10.1137/0217048 | ||||||||||||||||||||||
7 | SR | All Stable Pairs | N | N | Y | N | N | Finds all (if any) admitted stable pairs through enumeration. | https://doi.org/10.1137/0217048 | ||||||||||||||||||||||
8 | SR | Egalitarian Stable | N | N | Y | N | N | Produces an egalitarian stable matching, or reoprts that none exists. | https://doi.org/10.1137/0217048 | ||||||||||||||||||||||
9 | SR | Minimum Regret | N | N | Y | N | N | Produces a minimum regret stable matching, or reports that none exists. | https://mitpress.mit.edu/9780262515528/the-stable-marriage-problem/ | ||||||||||||||||||||||
10 | HA | Popular | Y | Y | Y | Y | N/A | Produces a popular matching or reports that none exists. | https://doi.org/10.1137/06067328X | ||||||||||||||||||||||
11 | HA | Rank-Maximal | Y | Y | Y | Y | N/A | Produces a rank-maximal matching. | https://doi.org/10.1145/1198513.1198520 | ||||||||||||||||||||||
12 | HA | Greedy | Y | Y | Y | Y | N/A | Produces a greedy maximum matching. | https://www.dcs.gla.ac.uk/~rwi/greedy.pdf | ||||||||||||||||||||||
13 | HA | Generous | Y | Y | Y | Y | N/A | Produces a generous maximum matching. | https://www.dcs.gla.ac.uk/~rwi/greedy.pdf | ||||||||||||||||||||||
14 | HA | Greedy-Generous | Y | Y | Y | Y | N/A | Produces a greedy-generous maximum profile. | https://www.dcs.gla.ac.uk/~rwi/greedy.pdf | ||||||||||||||||||||||
15 | HA | Minimum Cost | Y | Y | Y | Y | N/A | Produces a minimum cost maximum matching. | Folklore | ||||||||||||||||||||||
16 | HA | Naive | Y | Y | Y | Y | N/A | Produces a matching using the random serial dictatorship mechanism. | Folklore | ||||||||||||||||||||||
17 | HA | Popular Pairs | Y | Y | Y | N | N/A | Finds all admitted popular pairs. | https://doi.org/10.1007/s10878-009-9287-9 | ||||||||||||||||||||||
18 | HA | Visualise Switching Graph | Y | N | Y | Y | N/A | Visualises the switching graph for popular matchings. | https://doi.org/10.1007/s10878-009-9287-9 | ||||||||||||||||||||||
19 | HA | Maximum Cardinality Pareto Optimal | N | Y | Y | Y | N/A | Produces a maximum cardinality Pareto optimal matching. | https://doi.org/10.1007/978-3-540-30551-4_3 | ||||||||||||||||||||||
20 | HA | Number of Popular Matchings | N | Y | Y | N | N/A | Computes the number of popular matchings admitted by the instance. | https://doi.org/10.1007/s10878-009-9287-9 | ||||||||||||||||||||||
21 | HA | Minimum Cost Maximum Cardinality Popular | N | Y | Y | N | N/A | Produces a maximum cardinality popular matching with minimum cost. | https://doi.org/10.1007/s10878-009-9287-9 | ||||||||||||||||||||||
22 | HA | Rank-Maximal Popular | N | Y | Y | N | N/A | Produces a rank-maximal popular matching or reports that none exists. | https://doi.org/10.1007/s10878-009-9287-9 | ||||||||||||||||||||||
23 | HA | Generous Maximum Cardinality Popular | N | Y | Y | N | N/A | Produces a maximum cardinality popular matching with generous profile. | https://doi.org/10.1007/s10878-009-9287-9 | ||||||||||||||||||||||
24 | HA | Popular Uniform at Random | N | Y | Y | N | N/A | Produces a popular matching uniform at random, or reports that none exists. | https://doi.org/10.1007/s10878-009-9287-9 | ||||||||||||||||||||||
25 | HA | Enumerate all Popular Matchings | N | N | Y | N | N/A | Finds all admitted popular matchings. | https://doi.org/10.1007/s10878-009-9287-9 | ||||||||||||||||||||||
26 | HR | Kiraly One-Sided Ties | Y | Y | Y | Y | N/A | Produces an approximation for a maximum stable matching for instances with complete or incomplete lists and ties only on the hospital side. | https://doi.org/10.1007/978-3-540-87744-8_52 | ||||||||||||||||||||||
27 | HR | Kiraly Two-Sided Ties | Y | Y | Y | Y | N/A | Produces an approximation for a maximum stable matching for instances with complete or incomplete lists and ties on both sides. | https://doi.org/10.3390/a6030471 | ||||||||||||||||||||||
28 | HR | Super Stable | Y | N | Y | Y | N/A | Produces a super-stable matching, or reports that none exists. | https://doi.org/10.1007/3-540-44985-X_24 | ||||||||||||||||||||||
29 | HR | Strongly Stable | Y | N | Y | N | N/A | Produces a strongly stable matching in the SMTI context, or reports that none exists. | https://doi.org/10.1007/3-540-36494-3_39 | ||||||||||||||||||||||
30 | HR | No-Ties Stable | N | Y | Y | Y | N/A | Produces the resident-optimal stable matching. | https://doi.org/10.2307/2312726 | ||||||||||||||||||||||
31 | HR | Maximum Popular | N | N | Y | N | N/A | Produces a maximum popular matching in the SMI context. | https://doi.org/10.1016/j.ic.2012.10.012 | ||||||||||||||||||||||
32 | HR | All Stable Matchings (Rotations) | N | N | N | N | N/A | Finds all stable matchings via rotation elimination in the SM context (requires complete preference lists). | https://doi.org/10.1137/0216010 | ||||||||||||||||||||||
33 | HR | All Stable Matchings (Breakmarriage) | N | N | N | N | N/A | Finds all stable matchings using Algorithm Breakmarriage in the SM context (requires complete preference lists). | https://doi.org/10.1145/362619.362631 | ||||||||||||||||||||||
34 | HR | All Stable Pairs | N | N | N | N | N/A | Finds all stable pairs through enumeration in the SM context (requires complete preference lists). | https://doi.org/10.1137/0216010 | ||||||||||||||||||||||
35 | HR | Egalitarian Stable | N | N | N | N | N/A | Produces an egalitarian stable matching in the SM context (requires complete preference lists). | https://doi.org/10.1145/28869.28871 | ||||||||||||||||||||||
36 | HR | Minimum Regret | N | N | N | N | N/A | Produces a minimum regret stable matching in the SM context (requires complete preference lists). | https://doi.org/10.1137/0216010 | ||||||||||||||||||||||
37 | HR | Minimum Resident Regret | N | N | N | N | N/A | Produces a stable matching in the SM context with minimum resident regret (requires complete preference lists). | https://doi.org/10.1137/0216010 | ||||||||||||||||||||||
38 | HR | Minimum Hospital Regret | N | N | N | N | N/A | Produces a stable matching in the SM context with minimum hospital regret (requires complete preference lists). | https://doi.org/10.1137/0216010 | ||||||||||||||||||||||
39 | SPA | Cost-Optimal One-sided | Y | Y | Y | N/A | N/A | Produces a minimum cost maximum matching considering only student preferences. | https://doi.org/10.1007/978-3-319-19315-1_19 | ||||||||||||||||||||||
40 | SPA | Greedy One-Sided | Y | Y | Y | N/A | N/A | Produces a greedy maximum matching considering only student preferences. | https://doi.org/10.1007/978-3-319-19315-1_19 | ||||||||||||||||||||||
41 | SPA | Generous One-Sided | Y | Y | Y | N/A | N/A | Produces a generous maximum matching considering only student preferences. | https://doi.org/10.1007/978-3-319-19315-1_19 | ||||||||||||||||||||||
42 | SPA | Student-Optimal Stable | N | Y | Y | N/A | N/A | Produces the student-optimal stable matching. | https://doi.org/10.1016/j.jda.2006.03.006 | ||||||||||||||||||||||
43 | SPA | Lecturer-Optimal Stable | N | Y | Y | N/A | N/A | Produces the lecturer-optimal stable matching. | https://doi.org/10.1016/j.jda.2006.03.006 | ||||||||||||||||||||||
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46 | Acronyms | General Reference | |||||||||||||||||||||||||||||
47 | EGS | Extended Gale Shapley Algorithm | https://www.dcs.gla.ac.uk/research/algorithms/AMUP | ||||||||||||||||||||||||||||
48 | HA | House Allocation Problem | |||||||||||||||||||||||||||||
49 | HAT | House Allocation Problem with Ties | |||||||||||||||||||||||||||||
50 | HRT | Hospitals/Residents Problem with Ties | |||||||||||||||||||||||||||||
51 | MAX HROST | Maximum Cardinality Stable Matching in the Hospitals/Residents Problem with one sided Ties | |||||||||||||||||||||||||||||
52 | MAX HRT | Maximum Cardinality Stable Matching in the Hospitals/Residents Problem with Ties | |||||||||||||||||||||||||||||
53 | SM | Stable Marriage Problem | |||||||||||||||||||||||||||||
54 | SMT | Stable Marriage Problem with Ties | |||||||||||||||||||||||||||||
55 | SMI | Stable Marriage Problem with Incomplete Lists | |||||||||||||||||||||||||||||
56 | SMTI | Stable Marriage Problem with Ties and Incomplete Lists | |||||||||||||||||||||||||||||
57 | SR | Stable Roommates Problem | |||||||||||||||||||||||||||||
58 | SRI | Stable Roommates Problem with Incomplete lists | |||||||||||||||||||||||||||||
59 | SPA | Student-Project Allocation Problem | |||||||||||||||||||||||||||||
60 | SPA-S | Student-Project Allocation with Lecturer preferences over Students | |||||||||||||||||||||||||||||
61 | SPA-ST | Student-Project Allocation with Lecturer preferences over Students and Ties | |||||||||||||||||||||||||||||
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