منابع مشابه
Approximately Counting H-Colourings is #BIS-Hard
We consider the problem of counting H-colourings from an input graph G to a target graph H . We show that if H is any fixed graph without trivial components, then the problem is as hard as the well-known problem #BIS, which is the problem of (approximately) counting independent sets in a bipartite graph. #BIS is a complete problem in an important complexity class for approximate counting, and i...
متن کاملDetecting communities is Hard (And Counting Them is Even Harder)
We consider the algorithmic problem of community detection in networks. Given an undirected friendship graph G = (V, E), a subset S ⊆ V is an (α, β)-community if: • Every member of the community is friends with an α-fraction of the community; • Every non-member is friends with at most a β-fraction of the community. Arora et al [AGSS12] gave a quasi-polynomial time algorithm for enumerating all ...
متن کاملHow Hard Is Counting Triangles in the Streaming Model?
The problem of (approximately) counting the number of triangles in a graph is one of the basic problems in graph theory. In this paper we study the problem in the streaming model. We study the amount of memory required by a randomized algorithm to solve this problem. In case the algorithm is allowed one pass over the stream, we present a best possible lower bound of Ω(m) for graphs G with m edg...
متن کاملCounting Matchings of Size k Is W[1]-Hard
We prove #W[1]-hardness of the following parameterized counting problem: Given a simple undirected graph G and a parameter k ∈ N, compute the number of matchings of size k in G. It is known from [1] that, given an edge-weighted graph G, computing a particular weighted sum over the matchings in G is #W[1]-hard. In the present paper, we exhibit a reduction that does not require weights. This solv...
متن کاملApproximately Counting H-Colorings is $\#\mathrm{BIS}$-Hard
We examine the computational complexity of approximately counting the list H-colourings of a graph. We discover a natural graph-theoretic trichotomy based on the structure of the graph H . If H is an irreflexive bipartite graph or a reflexive complete graph then counting list H-colourings is trivially in polynomial time. Otherwise, if H is an irreflexive bipartite permutation graph or a reflexi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Information and Computation
سال: 1989
ISSN: 0890-5401
DOI: 10.1016/0890-5401(89)90063-1