اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRikudo is NP-complete
110
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Rikudo is a number-placement puzzle, where the player is asked to complete a Hamiltonian path on a hexagonal grid, given some clues (numbers already placed and edges of the path). We prove that the game is complete for NP, even if the puzzle has no hole. When all odd numbers are placed it is in P, whereas it is still NP-hard when all numbers of the form $3k+1$ are placed.
قيم البحث
اقرأ أيضاً
In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an $m times n$ grid of cells, where each cell possibly contains a clue among +, -, |. The goal is to partition the grid into disjoint rectangles, where every rectangle contains exac
tly one clue, rectangles containing + are square, rectangles containing - are strictly longer horizontally than vertically, rectangles containing | are strictly longer vertically than horizontally, and no four rectangles share a corner. We prove this puzzle NP-complete, establishing a Nikoli gap of 16 years. Along the way, we introduce a gadget framework for proving hardness of similar puzzles involving area coverage, and show that it applies to an existing NP-hardness proof for Spiral Galaxies. We also present a mathematical puzzle font for Tatamibari.
When can $t$ terminal pairs in an $m times n$ grid be connected by $t$ vertex-disjoint paths that cover all vertices of the grid? We prove that this problem is NP-complete. Our hardness result can be compared to two previous NP-hardness proofs: Lynch
s 1975 proof without the ``cover all vertices constraint, and Kotsuma and Takenagas 2010 proof when the paths are restricted to have the fewest possible corners within their homotopy class. The latter restriction is a common form of the famous Nikoli puzzle emph{Numberlink}; our problem is another common form of Numberlink, sometimes called emph{Zig-Zag Numberlink} and popularized by the smartphone app emph{Flow Free}.
209 -
Adrien Friggeri
, Eric Fleury (ENS / LIPn Laboratoire de lInformatique du Parallelisme / INRIA Grenoblen Rh^one-Alpes
2011
We show that the problem of finding a set with maximum cohesion in an undirected network is NP-hard.
We show the NP-completeness of the existential theory of term algebras with the Knuth-Bendix order by giving a nondeterministic polynomial-time algorithm for solving Knuth-Bendix ordering constraints.
This paper discusses the hardness of finding minimal good-for-games (GFG) Buchi, Co-Buchi, and parity automata with state based acceptance. The problem appears to sit between finding small deterministic and finding small nondeterministic automata, wh
ere minimality is NP-complete and PSPACE-complete, respectively. However, recent work of Radi and Kupferman has shown that minimising Co-Buchi automata with transition based acceptance is tractable, which suggests that the complexity of minimising GFG automata might be cheaper than minimising deterministic automata. We show for the standard state based acceptance that the minimality of a GFG automaton is NP-complete for Buchi, Co-Buchi, and parity GFG automata. The proofs are a surprisingly straight forward generalisation of the proofs from deterministic Buchi automata: they use a similar reductions, and the same hard class of languages.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
