Graph Sparsification by Effective Resistances
نویسندگان
چکیده
منابع مشابه
Uncertain Graph Sparsification
Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely expensive. Sparsification has often been used to reduce the size of deterministic graphs by maintaining only the important edges. However, adaptation of determi...
متن کاملar X iv : 0 80 3 . 09 29 v 2 [ cs . D S ] 7 M ar 2 00 8 Graph Sparsification by Effective Resistances ∗
We present a nearly-linear time algorithm that produces high-quality sparsifiers of weighted graphs. Given as input a weighted graph G = (V,E,w) and a parameter ǫ > 0, we produce a weighted subgraph H = (V, Ẽ, w̃) of G such that |Ẽ| = O(n logn/ǫ) and for all vectors x ∈ R (1 − ǫ) ∑ uv∈E (x(u)− x(v))2wuv ≤ ∑ uv∈Ẽ (x(u)− x(v))2w̃uv ≤ (1 + ǫ) ∑ uv∈E (x(u)− x(v))2wuv. (1) This improves upon the spars...
متن کاملar X iv : 0 80 3 . 09 29 v 1 [ cs . D S ] 6 M ar 2 00 8 Graph Sparsification by Effective Resistances ∗
We present a nearly-linear time algorithm that produces high-quality sparsifiers of weighted graphs. Given as input a weighted graph G = (V,E,w) and a parameter ǫ > 0, we produce a weighted subgraph H = (V, Ẽ, w̃) of G such that |Ẽ| = O(n logn/ǫ) and for all vectors x ∈ R (1 − ǫ) ∑ uv∈E (x(u)− x(v))2wuv ≤ ∑ uv∈Ẽ (x(u)− x(v))2w̃uv ≤ (1 + ǫ) ∑ uv∈E (x(u)− x(v))2wuv. (1) This improves upon the spars...
متن کاملar X iv : 0 80 3 . 09 29 v 4 [ cs . D S ] 1 8 N ov 2 00 9 Graph Sparsification by Effective Resistances ∗
We present a nearly-linear time algorithm that produces high-quality spectral sparsifiers of weighted graphs. Given as input a weighted graph G = (V, E, w) and a parameter ! > 0, we produce a weighted subgraph H = (V, Ẽ, w̃) of G such that |Ẽ| = O(n log n/!) and for all vectors x ∈ R (1 − !) ∑ uv∈E (x(u) − x(v))2wuv ≤ ∑ uv∈Ẽ (x(u) − x(v))2w̃uv ≤ (1 + !) ∑ uv∈E (x(u) − x(v))2wuv. (1) This improves...
متن کاملDistributed Graph Clustering and Sparsification
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of algorithmic design methods for graph clustering. Most of these methods, however, are based on complicated spectral techniques or convex optimisation, and cannot be d...
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: SIAM Journal on Computing
سال: 2011
ISSN: 0097-5397,1095-7111
DOI: 10.1137/080734029