The token swap problem: polynomial time algorithms for graph classes and integer linear programming formulations

dc.creatorCaio Henrique Segawa Tonetti
dc.date.accessioned2026-04-02T19:50:35Z
dc.date.issued2022-02-21
dc.description.abstractO framework de reconfiguração introduz o conceito de transformação em problemas computacionais, mostrando novas preocupações como resultado da necessidade de compreender estas mudanças sob uma variedade de operações e restrições. Esta dissertação estuda o problema de Token Swap, um tipo de tarefa de reconfiguração em que começamos com fichas distribuídas nos vértices de um grafo e buscamos movê-las até que cada ficha alcance o vértice alvo que lhe corresponde. O objetivo é realizar essa transformação usando o menor número possível de operações de troca. O principal resultado dessa dissertação é a construção das ferramentas matemáticas necessárias e da prova de existência de um algoritmo ótimo para grafos da classe threshold e, subsequentemente, cografos. Então, alguns trabalhos preliminares sobre modelos de programação linear inteira para os problemas de Token Swap e Parallel Token Swap também são apresentados, juntamente com o raciocínio por trás de cada restrição.
dc.description.sponsorshipCAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
dc.identifier.urihttps://hdl.handle.net/1843/2340
dc.languageeng
dc.publisherUniversidade Federal de Minas Gerais
dc.rightsAcesso aberto
dc.rightsAttribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectComputação – Teses
dc.subjectArquitetura de computador – Teses
dc.subjectTeoria dos Grafos – Teses
dc.subjectProgramação linear – Teses
dc.subject.otherGraph theory
dc.subject.otherReconfiguration
dc.subject.otherInteger programming
dc.titleThe token swap problem: polynomial time algorithms for graph classes and integer linear programming formulations
dc.title.alternativeO problema da troca de tokens: algoritmos de tempo polinomial para classes de grafos e formulações de programação linear inteira
dc.typeDissertação de mestrado
local.contributor.advisor-co1Sebastián Alberto Urrutia
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local.contributor.advisor1Vinicius Fernandes dos Santos
local.contributor.advisor1Latteshttps://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4756555E8&tokenCaptchar=0cAFcWeA63d5RsM9q9wajCYXoNIDy2HLmZJK8CjxZOCcBN5XLdaPVriDWKSLsyqPUgvE0L7GvwkPi0cowYF54wp3DuH6-wEj4C40ajTsyt_It2Q2BfbFY8R4V-8SS_Pwh72kgeMTuFNujaOTuFhCqzaQcIPbtBrYezJWvuLQhna2_bGqQejqsvZcarw-fV21BW3TKGKnkf9Py2-X5oEDEbhr02_BeEcLKEaQ2IsStYbeDRuLEBT4vDIwmNlFqcXl3Q1scWPxZa02AssE2BkIY46GsWRksA7RmwzhIbJzVVNpgq-zRQpjsZlEtKM8_8UTSs05f8JPa-HtJrtkUwEJgGHon7oBS84l90A6SDA54m3Rd9ygp2eZfYMOlI7aD6oq7SnaaisLnXO_oH4x8hKFRMMV4dQjm8Bo1_xiVGWNpHeA3DUFnYLi2DYGfMnhXcQwxcCPDpy-IRcgC8osj2IdJEWj5It3xQM7Wh6I6ZYqgmaJcj8PM9IgNeTu_liPeLqqcDsfSG84k8f8_EupLvIUAqQ2ug45dn-vf-RHiKYzCyjc4rR5q_JHUZNDsO7fPb9r67SoF8rhGoE-4anZq6ySMJRzJVlSahhIuGn_yg_e2RdPeCcZJeXr2Ty1KUuRGpl4vxwXXkjaYw_Q5Iv2BfaSYq9QRw6T3PwjgVCDH0jWac60HUWxIimT50GKXRzwSwiLq3HzkAjm6goOPVJfUaFfasVi1g_jCv7C8jsgz67EaAXbSgXuL9TWbzuUBU0mmsSwKOTbdHBJdDRoS64eSmtghJzNFMG578HqUWHkOp-IARc54z7QhswJcT07DeoibCo04VzF75CtbL7EWuudQ3KxEHcU-xYCKUApqeMs6TgBxp2mKN5QE6zhMeenSxeJWzFt3zi5LTzNkRXc2ubfJT9ApKRkGZyGsvaGB1rh6_u4-zPUL7WDp_tw6Gt4q0DmYuPTO8tIKwNXgINkVUOT2xPJBs8Z0dkMWwd4-kHY4QhgIOY_4oj0kFLmQ6NVf94-sMiN4mTRixkk3XWcJQOpfrdgO5gaseYkc6xr9r6AUQPWZ7bnREZ23k-QrIR903Y75CIgIfUiX-u0O7UD-sMhogGslMyMEevY4xbKxkrNnu94ebGLKgXn-oxmUxSLWf0xd-8ifFizHfwvbMYt5Sh_P126PFqajVmW3jNg8mGhmOjy9uCJb99lxSzpqwCv6cy6HUxJkcxorBE9b8FTpeLBJkt6dcvIwfCjJA-zwW20WHt8BXl-ng8v-0pGk4xTNNemUOQ_Vu8UPrIP006DjnXGrxf0yQxfIMwMeRurNh2xf67qOfR29AzP463HctkLFOGPPXx0as62NO-VdbTXnMrM1rve5F1gYE7sEAzvnKMIYxcPPXp966P8TchgwmTe1IYspqn5eX6NpmGfTyAY5kM8rYCOdj8Lv6HhB2bf6qqV1S9lyZ3YzA1iGmwq40GPL-Fv_sL784fPRZ0XP0wQdzyG-SPVqBWW_BZHD2tUAksd2oGnKyT_ZrAw9rYSMDUR8eYIF_WThJECJQOERu_zt9755zjsguXsUaCaRjvmm3WzkikbdGwI6adt2_o1w6PvAmOtg2braeucAw2Vsw5Cjb7Efjvv1ouFSLR_v6VMocxL-ZhQT-_6_I3S-7D1Qd7a9kTWGyL7kExyW66PdPBBqEIet9HkqWao_9Y1Npt_YlWXWmNpZY1LOD8TzwHZz-tJtxQSol_aUXxV_dz2tbKDJ7gqE3L06_pb9mMMjrkLRI0E-yXCIBtAFQNXMZ0AVMIYRBb2M-zjwInYvg7lBSfIdTvGxnpJPJhkLPX8ew6klKIe_ZT2AFpBfN-GThbiYy9bXjF8Mjzy5NxFnHcZ_lEMvDsa9kvWh7KRxkZq5rwy9DtL9julhWAq5bPCsYWLB4teb0LBz42xPKkrCsZPbGOx6Cybia69fMswokBN5PU1zAvrr1Y-ENov_HPU0giAAbmQqqwVjyUfdLshtqqaiBVhu7twzJx97fEh9LmCZAxyalHiVpX_xArhZ5r_3y9yPNBTcFjOwmOx8_3qqM86FmbfX6IWqtoIXxxGR4UYESAaukmeQfNKW6I1lK-Nj5YJDNd_B5ufqu0ZEbnm7pY2B006N52uG3UYW-hv64GcLd2jUZ9rbT7Xqi1gN2LKbMDs-UownB6tGI8ZblN2Ew4xzkpLUo3KoRol82m5FxLGcx6GmXbA
local.contributor.referee1Celina Miraglia Herrera de Figueiredo
local.contributor.referee1Fernando Magno Quintão Pereira
local.creator.Latteshttps://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4302751Y8&tokenCaptchar=0cAFcWeA6co0CNReQQIC9fc74GDl_yEqwZrLN0N71HWjBexfV39OzL8s113YrWtNsR7Xg2Y_mLRvbVe9YekNGOhnyNMMvAjlE2ORjOcyCwfELzXMlFAx53f854mkatRY381bRfediFtrP9wWdNJVYg5ixmklcUS05_25QeMzzmOXqc8RnbUSMmgKOcUj_PoGsRUcfovT4lmGlDsXXtfh3Hm3-b61-vEethD6mA0tcD_Op8ZLfMDaXpxCR5PKDmDUzHnKvSxfbWdCbmMBSaOqa_zSZtZIPYsFUkInncJIvj9m1-kjBq8ZfdKmJRHiFiKO1Dp6WVUM7YdylWNgBiZN_U6_Y_4HWoyrsm5E6Gv9dFDGK5brhUirnA_avIAzDi-6Ef-m5JDjF-MvS8ztzi-fHGvJOqAL5jU1t0YZxo4SJf702_buKA9SxY8rzSDC8drOAEWaWszz69MxBAzsGW16Aqn_12v2xaARxoqbu85XzZsVS1J6OtKzBXae98wFwu78En3VxLT9qSLSDxgWxozarAVTDIGL1Yvx_uUBxz2F3mvDwLqk_ay4fqGIzApWbSk6sQQbsCtGIQU2OgoLmLnTtovVd_bX-XtJnCjvTXZWRKvtfpNg_SUHWHmboDGDevbvbBnfIbZNN6WsKtpG84Fmx1mohvGmCWaSAEEHbE3yt9NP4tosmCfJslS-7oBWg85UNOl01vUAWos41lxY5fyBHGpALabxKJbVTwAzXEDzXxjFYQu4cuZvl8649D6OOOnSCNoK3YkF6WplpoiM5rwPAe5s2ehTpIQKUl1boJvND1_SX_EJCX6WYjtpxREuA9S9vA4GC0jgrnexMgG9gxiRyXE9LXqXvTlK8ybljiycWedZPoelyTejoU95-sXI_QP-JYTbrp7svjN4df6dG7d-0TrnHdWqypraWwU-qopaULOg4lGnFRBCDwwdcHmjiMD_kDP00y1P1lu7P4P4UFtslbkUwSR1gfcJs6qA5wbXOyMdX8ZQ2rr3uEytzyd08g0QgieC8wH6CtN3fV0Yaonohjjg_k1OcjgC_Jw-OgRxvg1Z-nJGEJCJT4N236P2WynfQDWm1HtXx4Rd5PUE_79VYke9C827l1U7lwAPfMk7wo4tcXkktVJq--ldlxBKzKj5xW5ah_5shCGu8qzCH41A4iufHwmigurF7RsE34cvr8K1GBRpxDdAm5b_Fhb6dHzfIECm6vv2ONLVAvjoJ7l2GtWeiM3nGCd2w5ICtELCNrqC_-Nzm3WhgX__sMqwepQlFIHe4h2_O8jWBb5IWihaOto0UCLz5MKuAiCP0rPC4sp7EZ_WfKOiwbgZqNHxZWm1cO4wyFTjxSJyyn3elwi_R3j_2QW0qb1C8WU2eOThqrMcGbn09QahJ6P1QwSBvyvofP8hLS2MoeblgYP1EnxIusuzuLdAx5EEvAnyGngWTjCHoGUDqwIt1wr9tMfTSXXLxcNq3jgnm2bR6qFUMBTkqSINr7XWU5J9TC42MzjJx7tNfae_wEfbVT03IS3QNDRfrBdXHN4zGuZC2KwGERizjqCwwLIkQ3cc_cNjby0EAHNp4VszQU4aKPVHUwffI4uxxj8ZiB9DUB1koTYJaWvzuXb8C9c4L2c-xlxpkjZhw4hDkQtBFURNh4zNwOYlALztw851ePfLosLLIvdKYQdcgn1c04LTtN-3SBvwtEmdBP1uudOzmPeo1OaP76BQYgUu0LUhu82eb718tcRXQBmD-xoHbOmVh-fPficqUpFiDhygYK-uT0XbYteI0_MIkDYLtnxO9vQ5fSZyhCIg0O5037nSfDIM97hBGYiYLzJJ03mTkNrSDQ36wghTYz4mo5IU3JXLeI74W_MmiBtmbAsOFWQDYQ4ESGqTigLcQbkH-Hn2NNUnOzthdEOfmN-0Qm4btX20rZxDY8EM0JZhFld8-lA0zJjUw5sCKqcWzTyLfG5rG7GD138DqL48WFa6n08-jjf1hYiHzaWIVRydni18ypX8sU3geBhAGi-KGHlDlQBRtRsgiKNTn8sYNPYWcM0eZd2RoUyfc5w7c6kXvLoqJNLQYouyfuyBNVDA
local.description.resumoThe reconfiguration framework introduces the concept of transformation into computational issues, posing new concerns as a result of the need to comprehend these changes under a variety of operations and constraints. This dissertation studies the Token Swap problem, a type of reconfiguration problem in which we start with tokens placed on the vertices of a graph and aim to move them so that each token ends up on its correct target vertex. The objective is to achieve this using as few swap operations as possible. The main result of this dissertation is the construction of the necessary mathematical tools and the proof of existence of an optimal algorithm for the class of threshold graphs and subsequently cographs. Then, some preliminary work on integer linear programming models for the problems of Token Swap and Parallel Token Swap will also be presented, together with a simple reasoning behind each constraint.
local.identifier.orcidhttps://orcid.org/0000-0001-9116-5801
local.publisher.countryBrasil
local.publisher.departmentICX - DEPARTAMENTO DE CIÊNCIA DA COMPUTAÇÃO
local.publisher.initialsUFMG
local.publisher.programPrograma de Pós-Graduação em Ciência da Computação
local.subject.cnpqCIENCIAS EXATAS E DA TERRA

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