关于计数欧拉回路的注记
Note on Counting Eulerian Circuits
摘要：
我们证明了无向图中欧拉回路数的计数问题对于P类是完全的。
英文摘要：
We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Beyond #CSP: A Dichotomy for Counting Weighted Eulerian Orientations with ARS
We define and explore a notion of unique prime factorization for constraint functions, and use this as a new tool to prove a complexity classification for counting weighted Eulerian orientation problems with arrow reversal symmetry (ARS). We prove that all such problems are either polynomial-time computable or #P-hard. We show that the class of weighted Eulerian orientation problems subsumes all weighted counting constraint satisfaction problems (#CSP) on Boolean variables. More significantly, we establish a novel connection between #CSP and counting weighted Eulerian orientation problems that…
cs.CC
欧拉定向与哈达玛码：通过计数建立的一种新联系
Eulerian orientations and Hadamard codes: A novel connection via counting
University of Science and Technology of China（中国科学技术大学）；Hefei National Laboratory（合肥国家实验室）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
研究通过对顶点施加局部约束函数的欧拉定向计数问题，发现欧拉定向与哈达玛码新联系，给出两类特殊约束函数及连锁反应算法，证明部分情况可多项式时间求解，两类函数同时出现时#EO问题是#P - 难的，建立了二者间新联系。
cs.CC
The Complexity of Counting Eulerian Tours in 4-Regular Graphs
We investigate the complexity of counting Eulerian tours ({\sc #ET}) and its variations from two perspectives---the complexity of exact counting and the complexity w.r.t. approximation-preserving reductions (AP-reductions \cite{MR2044886}). We prove that {\sc #ET} is #P-complete even for planar 4-regular graphs. A closely related problem is that of counting A-trails ({\sc #A-trails}) in graphs with rotational embedding schemes (so called maps). Kotzig \cite{MR0248043} showed that {\sc #A-trails} can be computed in polynomial time for 4-regular plane graphs (embedding in the plane is equivalent…
cs.CC
基于拟多态性视角的欧拉定向计数的线性规划算法
An LP Algorithm for Counting Eulerian Orientations Through the Lens of Quasi-polymorphism
本文针对带权欧拉定向计数的FP^NP侧情况，提出基于线性规划松弛的多项式时间算法，解决其是否属于FP的问题，得到完整的FP与#P二分结果。
cs.CCcs.DS
A short note on the counting complexity of conjunctive queries
This note closes a minor gap in the literature on the counting complexity of conjunctive queries by showing that queries that are not free-connex do not have a linear time counting algorithm under standard complexity assumptions. More generally, it is shown that the so-called quantified star size is a lower bound for the exponent in the runtime of any counting algorithm for conjunctive queries.
cs.CCcs.DBcs.LO
Note on "The Complexity of Counting Surjective Homomorphisms and Compactions"
Focke, Goldberg, and Živný (arXiv 2017) prove a complexity dichotomy for the problem of counting surjective homomorphisms from a large input graph G without loops to a fixed graph H that may have loops. In this note, we give a short proof of a weaker result: Namely, we only prove the #P-hardness of the more general problem in which G may have loops. Our proof is an application of a powerful framework of Lovász (2012), and it is analogous to proofs of Curticapean, Dell, and Marx (STOC 2017) who studied the "dual" problem in which the pattern graph G is small and the host graph H is the input. I…
cs.CC
更多相关论文收起更多论文
On the complexity of counting feedback arc sets
In this note we study the computational complexity of feedback arc set counting problems in directed graphs, highlighting some subtle yet common properties of counting classes. Counting the number of feedback arc sets of cardinality $k$ and the total number of feedback arc sets are #P-complete problems, while counting the number of minimum feedback arc sets is only proven to be #P-hard. Indeed, this latter problem is #.OptP[log n]-complete, hence if it belongs to #P then P=NP.
cs.CCcs.DM
Efficient Quantile Computation in Markov Chains via Counting Problems for Parikh Images
A cost Markov chain is a Markov chain whose transitions are labelled with non-negative integer costs. A fundamental problem on this model, with applications in the verification of stochastic systems, is to compute information about the distribution of the total cost accumulated in a run. This includes the probability of large total costs, the median cost, and other quantiles. While expectations can be computed in polynomial time, previous work has demonstrated that the computation of cost quantiles is harder but can be done in PSPACE. In this paper we show that cost quantiles in cost Markov ch…
cs.CCcs.DMcs.FL
The Complexity of Counting Edge Colorings and a Dichotomy for Some Higher Domain Holant Problems
We show that an effective version of Siegel's Theorem on finiteness of integer solutions and an application of elementary Galois theory are key ingredients in a complexity classification of some Holant problems. These Holant problems, denoted by Holant(f), are defined by a symmetric ternary function f that is invariant under any permutation of the k >= 3 domain elements. We prove that Holant(f) exhibits a complexity dichotomy. This dichotomy holds even when restricted to planar graphs. A special case of this result is that counting edge k-colorings is #P-hard over planar 3-regular graphs for k…
cs.CC
