We prove that the classic 1994 Taito video game, known as Puzzle Bobble or Bust-a-Move, is NP-complete. Our proof applies to the perfect-information version where the bubble sequence is known in advance, and it uses just three bubble colors. “A girl runs up with somethin’ to prove. So don’t just stand there. Bust a move!” — Young MC [YDD89]

a Graduate Aeronautical Laboratories and Department of Mechanical and Civil Engineering, Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena, CA 91125, USA b NJU-ECE Institute for Underground Space and Geo-environment, School of Earth Sciences and Engineering, Nanjing University, Nanjing, China, 210093 c Ecole Polytechnique Fédérale de Lausanne (EPFL), Sch...

AbstractFor the List Accessing Problem, Move-To-Front (MTF) algorithm has been proved to be the best performing online list accessing algorithm till date in the literature[10]. In this paper, we have made a comprehensive analysis of MTF algorithm and developed an Improved-MTF (IMTF) offline algorithm. We have generated two new types of data set and devise a new method of experimental analysis f...

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We …rst establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payo¤s. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated mark...

A 3-manifold with marked boundary is a pair (M, X), where M is a compact 3-manifold whose (possibly empty) boundary is made up of tori and Klein bottles, and X is a trivalent graph that is a spine of ∂M . A standard skeleton of a 3-manifold with marked boundary (M, X) is a standard sub-polyhedron P of M such that P ∩∂M coincides with X and with ∂P , and such that P ∪ ∂M is a spine of M \ B (whe...

A multiple-partners assignment game with heterogeneous sales and multiunit demands consists of a set of sellers that own a given number of indivisible units of (potentially many di¤erent) goods and a set of buyers who value those units and want to buy at most an exogenously …xed number of units. We de…ne a competitive equilibrium for this generalized assignment game and prove its existence by u...