[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82470-en":3,"doc-seo-82470-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82470,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Dual-Informed Vertical Expansion for Multi-Objective Node Selection in Anytime Conflict-Based Search","Conflict-Based Search (CBS) is an exact algorithm for Multi-Agent Path Finding (MAPF), yet its high-level node-selection rule is often fixed. The work treats node selection as a first-class design choice and proposes Dual-Informed Vertical Expansion (DIVE), which performs depth-oriented dives from the best-bound frontier while exploiting parent-child locality and using incumbent pruning. A branch-and-bound formalization proves traversal changes preserve exactness, and analyzes trade-offs among expanded nodes, dive breaks, queue size, and primal-dual bound progress. Experiments on MAPF benchmarks validate reduced dive breaks, earlier incumbents with certified gaps, and lower memory than best-first.","Dual-Informed Vertical Expansion for  \nMulti-Objective Node Selection in Anytime Conflict-Based Search  \nWillem van Osselaer, Jiarui Li, Meshal Alharbi, and Gioele Zardini  \narXiv :2607 .00156v1 [ cs .RO] 30 Jun 2026  \nAbstract—Conflict-Based Search (CBS) is a leading exact algorithm for Multi-Agent Path Finding (MAPF), but its high-level node-selection rule is usually treated as a fixed implementation detail. Standard best-first selection is strong for minimizing expanded nodes and closing the optimality certificate, yet it can maintain a large frontier, interrupt parent-child expansion sequences, and provide no feasible incumbent until termination. This paper studies node selection as a first-class design choice for exact CBS. We introduce Dual-Informed Vertical Expansion (DIVE), a policy that is best-bound between dives and depthoriented within a dive. DIVE starts each dive from the current best-bound frontier, follows promising children to exploit parentchild locality, and uses incumbent pruning to limit unproductive excursions. We formalize CBS node selection through a branchand-bound view, prove that the traversal policy can be changed without affecting exactness, and analyze the resulting trade-offs among expanded nodes, dive breaks, queue size, and primaldual bound progress. The analysis predicts three complementary extremes. Best-first search is node efficient, iterative deepening is memory efficient, and DIVE is dive efficient while retaining regular best-bound reanchoring. Experiments on standard MAPF benchmarks support this trade-off map. DIVE consistently reduces dive breaks, provides early incumbents with certified gaps, uses substantially less queue memory than best-first search, and benefits from warm starts and simple responsive variants in dense or memory-limited regimes.  \nI. INTRODUCTION  \nCOORDINATING many robots through a shared envi  \nronment is a core problem in robotics, with applications ranging from warehouse automation to airport surface operations and other graph-structured routing domains [1],[2] . Multi-Agent Path Finding (MAPF) captures this problem through a compact abstraction. Each agent must move from a start vertex to a goal vertex, agents may not collide, and the objective is to minimize a global cost such as the sum of arrival times. The abstraction is simple, but optimal routing is computationally hard [3] . For robotic systems that require certificates of optimality, predictable resource use, or meaningful behavior under time limits, the internal search policy of the solver becomes as important as its final guarantee.  \nConflict-Based Search (CBS) is one of the most widely used exact approaches for optimal MAPF [4], and decomposes the problem into a high-level search over a Constraint Tree (CT) . Each node n represents a relaxed subproblem with additional  \nThe authors are with the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA (e-mails:{willemvo, jiarui01, meshal, [gzardini](gzardini}@mit.edu)[}](gzardini}@mit.edu)[@mit.edu](gzardini}@mit.edu)).  \nThis work was supported by Prof. Zardini’s grant from the MIT Amazon Science Hub, hosted in the MIT Schwarzman College of Computing, and the MIT Maritime Consortium. Van Osselaer was supported by the Office of Naval Research (ONR) through the National Defense Science & Engineering Graduate (NDSEG) Fellowship Program.  \n|  |\n| --- |\n| \u003Cbr> |\n| Each policy has a unique strength\u003Cbr>DIVE exploits parent-child efficiency |\n\n\n|  |\n| --- |\n| Intermediate solutions\u003Cbr>\u003Cbr>DIVE turns exact CBS into an anytime algorithm |\n\nFig. 1. Overview of the node-selection perspective developed in this paper. Top: BFS expands the best-bound frontier, DFS follows deep branches without reanchoring, ID performs repeated threshold-limited passes, and DIVE combines depth-oriented dives with best-bound reanchoring. Bottom left: these policies occupy different regions of the multi-objective design space induced ","cbCaimW85jbcvO7k","https://ap.wps.com/l/cbCaimW85jbcvO7k","pdf",3896521,1,19,"English","en",105,"# Introduction\n# Dual-Informed Vertical Expansion (DIVE) Overview\n## Branch-and-Bound View of Node Selection\n## Exactness and Trade-off Analysis\n# Experimental Results","[{\"question\":\"What problem does the paper address in Conflict-Based Search (CBS) for MAPF?\",\"answer\":\"It addresses how the CBS node-selection rule influences practical behavior, including frontier size, when feasible incumbents appear, and how quickly dual bounds move toward optimality.\"},{\"question\":\"How does DIVE differ from standard best-first node selection in CBS?\",\"answer\":\"DIVE alternates depth-oriented dives within a dive and reanchors to the current best-bound frontier, following promising children to exploit parent-child locality and using incumbent pruning to limit unproductive excursions.\"},{\"question\":\"What does the analysis claim about exactness when changing the traversal policy?\",\"answer\":\"The paper formalizes node selection through a branch-and-bound view and proves the traversal policy can be changed without affecting CBS 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problem does the paper address in Conflict-Based Search (CBS) for MAPF?","Question",{"text":75,"@type":76},"It addresses how the CBS node-selection rule influences practical behavior, including frontier size, when feasible incumbents appear, and how quickly dual bounds move toward optimality.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does DIVE differ from standard best-first node selection in CBS?",{"text":80,"@type":76},"DIVE alternates depth-oriented dives within a dive and reanchors to the current best-bound frontier, following promising children to exploit parent-child locality and using incumbent pruning to limit unproductive excursions.",{"name":82,"@type":73,"acceptedAnswer":83},"What does the analysis claim about exactness when changing the traversal policy?",{"text":84,"@type":76},"The paper formalizes node selection through a branch-and-bound view and proves the traversal policy can be changed without affecting CBS 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