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- Anand Louis
- STOC
- 2015

The celebrated Cheeger's Inequality [AM85,a86] establishes a bound on the expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying theâ€¦ (More)

- Ankit Aggarwal, Anand Louis, +4 authors Surabhi Jain
- IPCO
- 2010

- Anand Louis, Nisheeth K. Vishnoi
- SWAT
- 2010

We consider the Degree-Bounded Survivable Network Design Problem: the objective is to find a minimum cost subgraph satisfying the given connectivity requirements as well as the degree bounds on theâ€¦ (More)

Cheeger's fundamental inequality states that any edge-weighted graph has a vertex subset S such that its expansion (a.k.a. conductance) is bounded as follows: [ Ï†(S) def= (w(S,bar{S}))/(min set(w(S),â€¦ (More)

- Anand Louis, Konstantin Makarychev
- SODA
- 2014

Given a graph G, the sparsest-cut problem asks to find the set of vertices S which has the least expansion defined as Ï†G(S) def = w(E(S, SÌ„)) min{w(S), w(SÌ„)} , where w is the total edge weight of aâ€¦ (More)

- Anand Louis, Prasad Raghavendra, Santosh Vempala
- 2013 IEEE 54th Annual Symposium on Foundations ofâ€¦
- 2013

We study the complexity of approximating the vertex expansion of graphs G = (V, E), defined as Î¦V def = minSCV n . |N(S)|/(|S||V\S). We give a simple polynomialtime algorithm for finding a subsetâ€¦ (More)

- Ankit Aggarwal, Anand Louis, +4 authors Surabhi Jain
- Math. Program.
- 2013

We consider the facility location problem where each facility can serve at most U clients. We analyze a local search algorithm for this problem which uses only the operations of add, delete and swapâ€¦ (More)

- T.-H. Hubert Chan, Anand Louis, Zhihao Gavin Tang, Chenzi Zhang
- J. ACM
- 2018

The celebrated Cheegerâ€™s Inequality (Alon and Milman 1985; Alon 1986) establishes a bound on the edge expansion of a graph via its spectrum. This inequality is central to a rich spectral theory ofâ€¦ (More)

- Anand Louis
- ArXiv
- 2010

We give O(log n)-approximation algorithm based on the cut-matching framework of [10, 13, 14] for the computing the sparsest cut on directed graphs. Our algorithm uses only O(log n) single commodityâ€¦ (More)

- Anand Louis, Prasad Raghavendra, Prasad Tetali, Santosh Vempala
- APPROX-RANDOM
- 2011

We consider two generalizations of the problem of finding a sparsest cut in a graph. The first is to find a partition of the vertex set into m parts so as to minimize the sparsity of the partitionâ€¦ (More)