In this paper we study two-sided matching markets in which the participants do not fully know their preferences and need to go through some costly deliberation process in order to learn their preferences. We assume that such deliberations are carried out via interviews, thus the problem is to find a good strategy for interviews to be carried out in order to minimize their use, whilst leading to a stable matching. One way to evaluate the performance of an interview strategy is to compare it against a naïve algorithm that conducts all interviews. We argue however that a more meaningful comparison would be against an optimal offline algorithm that has access to agents' preference orderings under complete information. We show that, unless P=NP, no offline algorithm can compute the optimal interview strategy in polynomial time. If we are additionally aiming for a particular stable matching, we provide restricted settings under which efficient optimal offline algorithms exist.</p

Goldberg, PW

Manlove, D

Rastegari, B

arXiv

In this paper we study two-sided matching markets in which the participants do not fully know their preferences and need to go through some costly deliberation process in order to learn their preferences. We assume that such deliberations are carried out via interviews, thus the problem is to find a good strategy for interviews to be carried out in order to minimize their use, whilst leading to a stable matching. One way to evaluate the performance of an interview strategy is to compare it against a nave ïalgorithm that conducts all interviews. We argue however that a more meaningful comparison would be against an optimal offline algorithm that has access to agents' preference orderings under complete information. We show that, unless P= NP, no offline algorithm can compute the optimal interview strategy in polynomial time. If we are additionally aiming for a particular stable matching, we provide restricted settings 

Rastegari, Baharak

Goldberg, Paul W.

Manlove, David

Southampton (e-Prints Soton)

Preference elicitation in matching markets via interviews: a study of offline benchmarks

The stable marriage problem and its extensions have been

extensively studied, with much of the work in the literature

assuming that agents fully know their own preferences over

alternatives. This assumption however is not always practical

(especially in large markets) and agents usually need

to go through some costly deliberation process in order to

learn their preferences. In this paper we assume that such

deliberations are carried out via interviews, where an interview

involves a man and a woman, each of whom learns

information about the other as a consequence. If everybody

interviews everyone else, then clearly agents can fully learn

their preferences. But interviews are costly, and we may

wish to minimize their use. It is often the case, especially

in practical settings, that due to correlation between agents’

preferences, it is unnecessary for all potential interviews to

be carried out in order to obtain a stable matching. Thus

the problem is to find a good strategy for interviews to be

carried out in order to minimize their use, whilst leading to a

stable matching. One way to evaluate the performance of an

interview strategy is to compare it against a na¨ıve algorithm

that conducts all interviews. We argue however that a more

meaningful comparison would be against an optimal offline

algorithm that has access to agents’ preference orderings under

complete information. We show that, unless P=NP, no

offline algorithm can compute the optimal interview strategy

in polynomial time. If we are additionally aiming for a

particular stable matching (perhaps one with certain desirable

properties), we provide restricted settings under which

efficient optimal offline algorithms exist

Goldberg, Paul

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Preference Elicitation in Matching Markets Via Interviews: A Study of Offline Benchmarks

In this paper we study two-sided matching markets in which the participants do not fully know their preferences and need to go through some costly deliberation process in order to learn their preferences. We assume that such deliberations are carried out via interviews, thus the problem is to find a good strategy for interviews to be carried out in order to minimize their use, whilst leading to a stable matching. One way to evaluate the performance of an interview strategy is to compare it against a nave ïalgorithm that conducts all interviews. We argue however that a more meaningful comparison would be against an optimal offline algorithm that has access to agents' preference orderings under complete information. We show that, unless P=NP, no offline algorithm can compute the optimal interview strategy in polynomial time. If we are additionally aiming for a particular stable matching, we provide restricted settings under which efficient optimal offline algorithms exist

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                          Rastegari, B., Goldberg, P., & Manlove, D. (2016). Preference elicitation inmatching markets via interviews: a study of offline benchmarks (extendedabstract). 1393-1394.Peer reviewed versionLink to publication record in Explore Bristol ResearchPDF-documentThis is the author accepted manuscript (AAM). The final published version (version of record) is available onlinevia ACM DL at http://dl.acm.org/citation.cfm?id=2937029.2937176. Please refer to any applicable terms of useof the publisher.University of Bristol - Explore Bristol ResearchGeneral rightsThis document is made available in accordance with publisher policies. Please cite only the publishedversion using the reference above. Full terms of use are available:http://www.bristol.ac.uk/pure/about/ebr-termsPreference Elicitation in Matching Markets via Interviews:A Study of Offline BenchmarksBaharak RastegariSchool of Computing ScienceUniversity of GlasgowGlasgow, UKbaharak.rastegari@glasgow.ac.ukPaul GoldbergDept.of Computer ScienceUniversity of OxfordOxford, UKpaul.goldberg@cs.ox.ac.ukDavid ManloveSchool of Computing ScienceUniversity of GlasgowGlasgow, UKdavid.manlove@glasgow.ac.ukAbstractIn this paper we study two-sided matching markets in which theparticipants do not fully know their preferences and need to gothrough some costly deliberation process in order to learn theirpreferences. We assume that such deliberations are carried outvia interviews, thus the problem is to find a good strategy for in-terviews to be carried out in order to minimize their use, whilstleading to a stable matching. One way to evaluate the perfor-mance of an interview strategy is to compare it against a naı¨vealgorithm that conducts all interviews. We argue however that amore meaningful comparison would be against an optimal offlinealgorithm that has access to agents’ preference orderings undercomplete information. We show that, unless P=NP, no offlinealgorithm can compute the optimal interview strategy in poly-nomial time. If we are additionally aiming for a particular stablematching, we provide restricted settings under which efficient op-timal offline algorithms exist.Keywords Two-sided matching; preferences; interviews1 IntroductionTwo-sided matching markets model many practical settings, suchas corporate hiring and university admission [6, 3]. In the clas-sical stable marriage problem participants are partitioned intotwo disjoint sets, and each participant on one side of the mar-ket wishes to be matched to a candidate from the other side ofthe market and has preferences over potential matches. A match-ing is called stable if no pair of participants would prefer to leavetheir assigned partners to pair with each other. Gale and Shap-ley’s seminal paper [1] proposed a polynomial-time algorithm forfinding a stable matching; a rich literature has developed since.A key assumption in much of this literature is that all marketparticipants know their full preference orderings. However, asmarkets grow large (e.g., in the hospital-resident matching marketor college admission market [1, 3]) it quickly becomes impracti-cal for participants to assess their precise preference rankings. In-stead, participants usually start out with some partial knowledgeabout their preferences and need to perform some deliberationin order to learn their precise preference ordering. In this paperwe assume that deliberations are carried out via interviews. In-terviews are usually costly, therefore we wish to minimize theirusage.Any interviewing strategy leads to refinements of the partial or-ders contained in the original problem instance that representeduncertainty over the true preferences. A key aim could be to carryout sufficient interviews so as to arrive at an instance that admitsa super-stable matching µ. Informally speaking, super-stabilityensures that µ will be stable regardless of how the remaininguncertainty is resolved. The original instance need not admit asuper-stable matching (see [2] for an example) but we are guar-anteed that a super-stable matching is always achievable (e.g., byconducting all possible interviews). We seek a good strategy thatconducts as few interviews as possible so as to obtain a refinedinstance that admits a super-stable matching. In general any suchstrategy will be an online algorithm, since the next interview tobe carried out might depend on the results of previous ones.2 Preliminary definitionsSMP, SMTI and SMT In an instance of the Stable Marriageproblem with Partially ordered preferences (SMP), there are twosets of agents, namely a set of men M and a set of women W .Each agent a finds a subset of agents on the opposite side of themarket acceptable – we refer to these as a’s acceptable candi-dates. An agent a’s preferences over his/her acceptable candi-dates need not be strict. That is, given two candidates, a might beindifferent between them. We denote by I an instance of SMP,and by pa the partial orders that represent the preference orderingof agent a. A matching µ is a pairing of men and women suchthat each man is paired with at most one woman and vice versa,and no agent is matched to an unacceptable partner. A well stud-ied special case of SMP is the Stable Marriage problem with Tiesand Incomplete lists (SMTI). In SMTI, each agent has a partitionof acceptable candidates into ties such that he or she is indifferentbetween the candidates in the same tie but has a strict preferenceordering over the ties. The Stable Marriage problem with Ties(SMT) is the special case of SMTI in which each man finds eachwoman acceptable and vice versa.Interviews to refine the partial orders In a given instance I ofSMP in this paper, we assume that the partial preference order-ing profile represents the agents’ initial information state. That is,agents may not have enough information initially in order to ranktheir acceptable candidates in strict order. However each agenta has a strict preference ordering a over his or her acceptablecandidates, although s/he may not initially be aware of this en-1tire ordering. We let M,W denote the strict (true underlying)preference ordering profile of all agents. The task of the agentsis to learn enough information about their acceptable candidatesin order to refine their preferences, in a manner consistent withM,W , to obtain an SMP instance I ′ that admits a super-stablematching µ (thus µ will be stable with respect to M,W ).Following the model introduced in [4], we assume that in-stances can be refined through interviews. Each interview pairsone man m with one woman w. An interview is informative toboth parties involved. When agent a interviews ` candidates, thisresults in a new refined SMP instance which is exactly the sameas I except that a now has a strict preference ordering over the `interviewed candidates.Note that not all refinements of I can be reached by a set ofinterviews. We say that an SMP instance I ′ is an interview-compatible refinement of I if I ′ can be refined from I using in-terviews. We define the cost of I ′ to be the minimum number ofinterviews required to refine I into I ′.Definitions of the interview minimization problems The mo-tivating problem is as follows: given an instance I of SMP, findan interview-compatible refinement I ′ of minimum cost such thatI ′ admits a super-stable matching. Since the result of one in-terview might influence which interview/s to carry out next, anystrategy for carrying out interviews should be regarded as an on-line algorithm. Towards computing bounds for the competitiveratio of an online algorithm, the offline scenario is of interest,and that is what we consider in what follows. In the offline case,the mechanism designer is given M,W , the strict (true under-lying) preference ordering profile of the agents, and would liketo compute an optimal interviewing schedule, i.e., an interview-compatible refinement I ′ of I , such that M,W refines I ′. Thisis reflected in the definition of the following problem, namedMIN-ICR, which is an abbreviation for “Minimum-cost Inter-view Compatible Refinement problem”.Definition 1 An instance of MIN-ICR comprises a tuple(I,M,W ), where I is an instance of SMP and M,W is a strictpreference ordering profile that refines I . The problem is to findan interview-compatible refinement I ′ of I such that (i) M,Wrefines I ′, (ii) I ′ admits a super-stable matching, and (iii) I ′ isof minimum cost amongst interview-compatible refinements thatsatisfy (i) and (ii).It is sometimes the case that we aim for a particular matching,stable under M,W , that has some desirable properties, for ex-ample it is preferred to every other stable matching by women.The offline problem can then be viewed as a restricted variantof MIN-ICR where, in addition to I and M,W , we are alsoequipped with a matching µ. This is reflected in the definition ofthe following problem, named MIN-ICR-EXACT, which is an ab-breviation for “Minimum-cost Interview Compatible Refinementproblem with Exact matching”.Definition 2 An instance of MIN-ICR-EXACT comprises a tuple(I,M,W , µ), where I is an instance of SMP, M,W is a strictpreference ordering profile that refines I , and µ is a matching thatis weakly stable w.r.t.M,W . The problem is to find an interview-compatible refinement I ′ of I , such that (i) M,W refines I ′, (ii)µ is super-stable in I ′, and (iii) I ′ is of minimum cost amongstinterview-compatible refinements of I that satisfy (i) and (ii).3 ResultsIn the full version of this paper [5], we prove that MIN-ICR andMIN-ICR-EXACT are NP-hard even if I is an instance of SMTIin which each tie is of size at most 3. Further, we prove that bothproblems are NP-hard even for SMT instances, and even if allmen are indifferent between all women. The hardness proofs areby reduction from the Vertex Cover problem (VC).We then explore the tractability of MIN-ICR-EXACT undervarious restricted settings, using a reverse reduction from MIN-ICR-EXACT to VC to prove our claims. We show that MIN-ICR-EXACT is solvable in polynomial time under three differentrestrictions: (i) if one side has fully known strict preference or-dering, (ii) if I is an instance of SMTI in which ties are of size atmost 2, and (iii) if I is an instance of of SMTI in which all menare endowed with the same ties, as well as all women.4 Future workThe main direction is to investigate the online case, where the trueunderlying preferences are not known to the mechanism designer,with respect to measures such as the competitive ratio. Further-more, an important question is whether MIN-ICR is polynomial-time solvable under some restricted setting. Extending the knownresults on interviewing in stable marriage markets to many-to-onemarkets such as college admission is another important future di-rection. It is also interesting to study online algorithms in a settingwhere elicitation is taking place via comparison queries.Acknowledgments. We thank Rob Irving and Piotr Krysta for theuseful discussions and their valuable feedback. This work wassupported by EPSRC grants EP/K01000X/1 and EP/K010042/1,and COST Action IC1205.References[1] D. Gale and L. S. Shapley. College admissions and the sta-bility of marriage. Amer. Math. Monthly, 69:9–15, 1962.[2] R. W. Irving. Stable marriage and indifference. DiscreteApplied Math., 48(3):261–272, 1994.[3] D. F. Manlove. Algorithmics of Matching Under Preferences.World Scientific, 2013.[4] B. Rastegari, A. Condon, N. Immorlica, and K. Leyton-Brown. Two-sided matching with partial information. InProc. EC ’13, pp. 733–750. ACM, 2013.[5] B. Rastegari, P. Goldberg and D. Manlove. Preference elici-tation in matching markets via interviews: A study of offlinebenchmarks. CoRR abs/1602.04792, 2016.[6] A. Roth and M. Sotomayor. Two-Sided Matching: A Study inGame-Theoretic Modeling and Analysis. Cambridge Univer-sity Press, 1990.2

Preference elicitation in matching markets via interviews:a study of offline benchmarks (extended abstract)

In this paper we study two-sided matching markets in which the participants do not fully know their preferences and need to go through some costly deliberation process in order to learn their preferences. We assume that such deliberations are carried out via interviews, thus the problem is to find a good strategy for interviews to be carried out in order to minimize their use, whilst leading to a stable matching. One way to evaluate the performance of an interview strategy is to compare it against a naandiuml;ve algorithm that conducts all interviews. We argue however that a more meaningful comparison would be against an optimal offline algorithm that has access to agents' preference orderings under complete information. We show that, unless P=NP, no offline algorithm can compute the optimal interview strategy in polynomial time. If we are additionally aiming for a particular stable matching, we provide restricted settings under which efficient optimal offline algorithms exist.</p

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Preference elicitation in matching markets via interviews: a study of offline benchmarks (extended abstract)

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Preference Elicitation in Matching Markets via Interviews:A Study of Offline Benchmarks(Extended Abstract)Baharak RastegariSchool of Computing ScienceUniversity of GlasgowGlasgow, UKbaharak.rastegari@glasgow.ac.ukPaul GoldbergDept. of Computer ScienceUniversity of OxfordOxford, UKpaul.goldberg@cs.ox.ac.ukDavid ManloveSchool of Computing ScienceUniversity of GlasgowGlasgow, UKdavid.manlove@glasgow.ac.ukABSTRACTIn this paper we study two-sided matching markets in whichthe participants do not fully know their preferences and needto go through some costly deliberation process in order tolearn their preferences. We assume that such deliberationsare carried out via interviews, thus the problem is to finda good strategy for interviews to be carried out in order tominimize their use, whilst leading to a stable matching. Oneway to evaluate the performance of an interview strategy isto compare it against a na¨ıve algorithm that conducts allinterviews. We argue however that a more meaningful com-parison would be against an optimal oﬄine algorithm thathas access to agents’ preference orderings under completeinformation. We show that, unless P=NP, no oﬄine algo-rithm can compute the optimal interview strategy in poly-nomial time. If we are additionally aiming for a particularstable matching, we provide restricted settings under whichefficient optimal oﬄine algorithms exist.KeywordsTwo-sided matching; preferences; interviews1. INTRODUCTIONTwo-sided matching markets model many practical set-tings, such as corporate hiring and university admission [6,3]. In the classical stable marriage problem participants arepartitioned into two disjoint sets, and each participant onone side of the market wishes to be matched to a candidatefrom the other side of the market and has preferences overpotential matches. A matching is called stable if no pair ofparticipants would prefer to leave their assigned partners topair with each other. Gale and Shapley’s seminal paper [1]proposed a polynomial-time algorithm for finding a stablematching; a rich literature has developed since.A key assumption in much of this literature is that all mar-ket participants know their full preference orderings. How-ever, as markets grow large (e.g., in the hospital-residentmatching market or college admission market [1, 3]) it quicklybecomes impractical for participants to assess their preciseAppears in: Proceedings of the 15th International Conferenceon Autonomous Agents and Multiagent Systems (AAMAS 2016),J. Thangarajah, K. Tuyls, C. Jonker, S. Marsella (eds.),May 9–13, 2016, Singapore.Copyright c© 2016, International Foundation for Autonomous Agents andMultiagent Systems (www.ifaamas.org). All rights reserved.preference rankings. Instead, participants usually start outwith some partial knowledge about their preferences andneed to perform some deliberation in order to learn theirprecise preference ordering. In this paper we assume thatdeliberations are carried out via interviews. Interviews areusually costly, therefore we wish to minimize their usage.Any interviewing strategy leads to refinements of the par-tial orders contained in the original problem instance thatrepresented uncertainty over the true preferences. A key aimcould be to carry out sufficient interviews so as to arrive atan instance that admits a super-stable matching µ. Infor-mally speaking, super-stability ensures that µ will be stableregardless of how the remaining uncertainty is resolved. Theoriginal instance need not admit a super-stable matching(see [2] for an example) but we are guaranteed that a super-stable matching is always achievable (e.g., by conducting allpossible interviews). We seek a good strategy that conductsas few interviews as possible so as to obtain a refined in-stance that admits a super-stable matching. In general anysuch strategy will be an online algorithm, since the nextinterview to be carried out might depend on the results ofprevious ones.2. PRELIMINARY DEFINITIONSSMP, SMTI and SMT.In an instance of the Stable Marriage problem with Par-tially ordered preferences (SMP), there are two sets of agents,namely a set of men M and a set of women W . Each agenta finds a subset of agents on the opposite side of the marketacceptable – we refer to these as a’s acceptable candidates.An agent a’s preferences over his/her acceptable candidatesneed not be strict. That is, given two candidates, a mightbe indifferent between them. We denote by I an instance ofSMP, and by pa the partial orders that represent the pref-erence ordering of agent a. A matching µ is a pairing ofmen and women such that each man is paired with at mostone woman and vice versa, and no agent is matched to anunacceptable partner. A well studied special case of SMP isthe Stable Marriage problem with Ties and Incomplete lists(SMTI). In SMTI, each agent has a partition of acceptablecandidates into ties such that he or she is indifferent betweenthe candidates in the same tie but has a strict preference or-dering over the ties. The Stable Marriage problem with Ties(SMT) is the special case of SMTI in which each man findseach woman acceptable and vice versa.Interviews to refine the partial orders.In a given instance I of SMP in this paper, we assumethat the partial preference ordering profile represents theagents’ initial information state. That is, agents may nothave enough information initially in order to rank their ac-ceptable candidates in strict order. However each agent ahas a strict preference ordering a over his or her acceptablecandidates, although s/he may not initially be aware of thisentire ordering. We let M,W denote the strict (true un-derlying) preference ordering profile of all agents. The taskof the agents is to learn enough information about their ac-ceptable candidates in order to refine their preferences, in amanner consistent with M,W , to obtain an SMP instanceI ′ that admits a super-stable matching µ (thus µ will bestable with respect to M,W ).Following the model introduced in [4], we assume that in-stances can be refined through interviews. Each interviewpairs one man m with one woman w. An interview is infor-mative to both parties involved. When agent a interviews `candidates, this results in a new refined SMP instance whichis exactly the same as I except that a now has a strict pref-erence ordering over the ` interviewed candidates.Note that not all refinements of I can be reached by aset of interviews. We say that an SMP instance I ′ is aninterview-compatible refinement of I if I ′ can be refined fromI using interviews. We define the cost of I ′ to be the mini-mum number of interviews required to refine I into I ′.Definitions of the interview minimization problems.The motivating problem is as follows: given an instance Iof SMP, find an interview-compatible refinement I ′ of mini-mum cost such that I ′ admits a super-stable matching. Sincethe result of one interview might influence which interview/sto carry out next, any strategy for carrying out interviewsshould be regarded as an online algorithm. Towards comput-ing bounds for the competitive ratio of an online algorithm,the oﬄine scenario is of interest, and that is what we considerin what follows. In the oﬄine case, the mechanism designeris given M,W , the strict (true underlying) preference or-dering profile of the agents, and would like to compute anoptimal interviewing schedule, i.e., an interview-compatiblerefinement I ′ of I, such that M,W refines I ′. This is re-flected in the definition of the following problem, namedMin-ICR, which is an abbreviation for “Minimum-cost In-terview Compatible Refinement problem”.Definition 1. An instance of Min-ICR comprises a tu-ple (I,M,W ), where I is an instance of SMP and M,Wis a strict preference ordering profile that refines I. Theproblem is to find an interview-compatible refinement I ′ ofI such that (i) M,W refines I ′, (ii) I ′ admits a super-stable matching, and (iii) I ′ is of minimum cost amongstinterview-compatible refinements that satisfy (i) and (ii).It is sometimes the case that we aim for a particularmatching, stable under M,W , that has some desirable prop-erties, for example it is preferred to every other stable match-ing by women. The oﬄine problem can then be viewed asa restricted variant of Min-ICR where, in addition to I andM,W , we are also equipped with a matching µ. This isreflected in the definition of the following problem, namedMin-ICR-Exact, which is an abbreviation for “Minimum-cost Interview Compatible Refinement problem with Exactmatching”.Definition 2. An instance of Min-ICR-Exact comprisesa tuple (I,M,W , µ), where I is an instance of SMP, M,Wis a strict preference ordering profile that refines I, and µ isa matching that is weakly stable w.r.t. M,W . The problemis to find an interview-compatible refinement I ′ of I, suchthat (i) M,W refines I ′, (ii) µ is super-stable in I ′, and (iii)I ′ is of minimum cost amongst interview-compatible refine-ments of I that satisfy (i) and (ii).3. RESULTSIn the full version of this paper [5], we prove that Min-ICRand Min-ICR-Exact are NP-hard even if I is an instanceof SMTI in which each tie is of size at most 3. Further,we prove that both problems are NP-hard even for SMTinstances, and even if all men are indifferent between allwomen. The hardness proofs are by reduction from the Ver-tex Cover problem (VC).We then explore the tractability of Min-ICR-Exact un-der various restricted settings, using a reverse reduction fromMin-ICR-Exact to VC to prove our claims. We show thatMin-ICR-Exact is solvable in polynomial time under threedifferent restrictions: (i) if one side has fully known strictpreference ordering, (ii) if I is an instance of SMTI in whichties are of size at most 2, and (iii) if I is an instance of ofSMTI in which all men are endowed with the same ties, aswell as all women.4. FUTUREWORKThe main direction is to investigate the online case, wherethe true underlying preferences are not known to the mecha-nism designer, with respect to measures such as the compet-itive ratio. Furthermore, an important question is whetherMin-ICR is polynomial-time solvable under some restrictedsetting. Extending the known results on interviewing in sta-ble marriage markets to many-to-one markets such as col-lege admission is another important future direction. It isalso interesting to study online algorithms in a setting whereelicitation is taking place via comparison queries.Acknowledgments. We thank Rob Irving and Piotr Krystafor the useful discussions and their valuable feedback. Thiswork was supported by EPSRC grants EP/K01000X/1 andEP/K010042/1, and COST Action IC1205.REFERENCES[1] D. Gale and L. S. Shapley. College admissions and thestability of marriage. Amer. Math. Monthly, 69:9–15,1962.[2] R. W. Irving. Stable marriage and indifference. DiscreteApplied Math., 48(3):261–272, 1994.[3] D. F. Manlove. Algorithmics of Matching UnderPreferences. World Scientific, 2013.[4] B. Rastegari, A. Condon, N. Immorlica, andK. Leyton-Brown. Two-sided matching with partialinformation. In Proc. EC ’13, pp. 733–750. ACM, 2013.[5] B. Rastegari, P. Goldberg and D. Manlove. Preferenceelicitation in matching markets via interviews: A studyof oﬄine benchmarks. CoRR abs/1602.04792, 2016.[6] A. Roth and M. Sotomayor. Two-Sided Matching: AStudy in Game-Theoretic Modeling and Analysis.Cambridge University Press, 1990.

In this paper we study two-sided matching markets in which the participants do not fully know their preferences and need to go through some costly deliberation process in order to learn their preferences. We assume that such deliberations are carried out via interviews, thus the problem is to find a good strategy for interviews to be carried out in order to minimize their use, whilst leading to a stable matching. One way to evaluate the performance of an interview strategy is to compare it against a naïve algorithm that conducts all interviews. We argue however that a more meaningful comparison would be against an optimal offline algorithm that has access to agents' preference orderings under complete information. We show that, unless P=NP, no offline algorithm can compute the optimal interview strategy in polynomial time. If we are additionally aiming for a particular stable matching, we provide restricted settings under which efficient optimal offline algorithms exist

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Preference elicitation in matching markets via interviews: a study of offline benchmarks (extended abstract)

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