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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A 1.344-approximation algorithm for the vertex cover problem
顶点覆盖问题 1.344 近似算法
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2023/12/11
We present an algorithm for the vertex cover problem by combining the LP relaxation and the random edge-reductions. The algorithm has the expected approximation ratio of 1.344.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Streaming algorithm for submodular cover problem
子模块化 覆盖问题 流算法
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2023/5/15
In this work, we mainly investigate the problem that minimizes the price function such that the valuation function exceeds a required threshold in submodular cover problem, where the price function is...
Cover times for sequences of Markov chains on random graphs
Random walk Cover time Maximal hitting time Random graph
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2012/6/15
We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (type 1) is the class of cover times approximated by the maximal hitting times s...
Rings over which every module has a flat $δ$-cover
-covers -perfect rings -semiperfect rings Flat modules
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2011/8/25
Abstract: Let $M$ be a module. A {\em $\delta$-cover} of $M$ is an epimorphism from a module $F$ onto $M$ with a $\delta$-small kernel. A $\delta$-cover is said to be a {\em flat $\delta$-cover} in ca...
The double cover of cubic surfaces branched along their Hessian
double cover cubic surfaces branched
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2011/2/23
We prove the relation between the Hodge structure of the double cover of a nonsingular cubic surface branched along its Hessian and the Hodge structure of the triple cover of P3 branched along the cub...
Minimum k-path vertex cover
Minimum k-path vertex cover
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2011/1/20
A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by k(G)the minimum cardinality of a k-path vertex cover i...
Determining When The Universal Abelian Cover of a Graph Manifold is a Rationla Homology Sphere
Universal Abelian Cover Graph Rationla Homology Sphere
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2010/11/8
It was shown in my earlier article that the splice diagram of a rational homology sphere graph manifold determines the manifolds universal abelian cover. In this article we use the proof of this to g...
Splice Diagram Singularities and The Universal Abelian Cover of Graph Orbifolds
Splice Diagram Singularities The Universal Abelian Cover of Graph Orbifolds
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2010/11/9
Given a rational homology sphere M, whose splice diagram satisfy the semigroup condition, Neumann and Wahl were able to define a complete intersection surface singularity called splice diagram singul...
Linear Cover Time is Exponentially Unlikely
Linear Cover Time Exponentially
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2010/11/19
We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small.
More precisely, for every D and C, there exists a=a(D,C)>0 such t...
Bordered Floer homology and the branched double cover I
Floer homology branched double cover I
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2010/11/9
Given a link in the three-sphere, Z. Szab\'o and the second author constructed a spectral sequence starting at the Khovanov homology of the link and converging to the Heegaard Floer homology of its br...
Threefolds with quasi-projective universal cover
universal cover L2-theory geometric orbifolds MMP
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2010/12/9
We study compact Kähler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from L2-theory, Campana’s geometric orbifolds and the minimal ...
Dense graphs with a large triangle cover have a large triangle packing
Dense graphs with large triangle cover large triangle packing
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2010/11/29
It is well known that a graph with m edges can be made triangle-free by removing (slightly less
than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make
triangle-f...
The Barrier Cone of a Convex Set and the Closure of the Cover
convex set barrier cone recession cone cover polar cone
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2009/1/22
For an arbitrary non-empty closed convex set $A$ in $\mathbb{R}^n$, we prove that the polar of the difference between the barrier cone $\mathbb{B}(A)$ and its interior $\text{int } \mathbb{B} (A)$ co...
Cover for Modules and Injective Modules
Commutative ring D-prime module cover prime submodule injective module quasi-injective and injective hull
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2010/2/25
Let R be a commutative ring with identity and M be an R-module with Spec(M) \neq f. A cover of the R-submodule K of M is a subset C of Spec(M) satisfying that for any x \in K, x \neq 0, there is N \in...