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Arora, Rao and Vazirani [2] showed that the standard semi-definite programming (SDP) relaxation of the Sparsest Cut problem with the <i>triangle inequality</i> constraints has an integrality gap of O(√log n). They conjectured that the gap is bounded from above by a constant. In this paper, we disprove this conjecture (referred to as the… (More)

- Rishi Saket, Nicolas Navet
- J. Embedded Computing
- 2006

- Venkatesan Guruswami, Rishi Saket
- ICALP
- 2010

Computing a minimum vertex cover in graphs and hypergraphs is a well-studied optimizaton problem. While intractable in general, it is well known that on bipartite graphs, vertex cover is polynomial time solvable. In this work, we study the natural extension of bipartite vertex cover to hypergraphs, namely finding a small vertex cover in kuniform k-partite… (More)

- Subhash Khot, Rishi Saket
- 2014 IEEE 55th Annual Symposium on Foundations of…
- 2014

We show that it is quasi-NP-hard to color 2-colorable 12-uniform hypergraphs with 2(log n) O(1) colors where n is the number of vertices. Previously, Guruswami et al. [1] showed that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with 22 O(vlog log n) colors. Their result is obtained by composing a standard Outer PCP with an Inner PCP based… (More)

- Rishi Saket
- 2014 IEEE 29th Conference on Computational…
- 2014

This work revisits the PCP Verifiers used in the works of Hastad [1], Guruswami et al. [2], Holmerin [3] and Guruswami [4] for satisfiable MAX-E3-SAT and MAX-EkSET-SPLITTING, and independent set in 2-colorable 4-uniform hypergraphs. We provide simpler and more efficient PCP Verifiers to prove the following improved hardness results: Assuming that NP… (More)

- Subhash Khot, Rishi Saket
- 2009

We construct integrality gap instances for SDP relaxation of the MAXIMUM CUT and the SPARSEST CUT problems. If the triangle inequality constraints are added to the SDP, then the SDP vectors naturally define an n-point negative type metric where n is the number of vertices in the problem instance. Our gap-instances satisfy a stronger constraint that every… (More)

- Subhash Khot, Preyas Popat, Rishi Saket
- APPROX-RANDOM
- 2010

In this paper, we investigate whether a constant round Lasserre Semi-definite Programming (SDP) relaxation might give a good approximation to the UNIQUE GAMES problem. We show that the answer is negative if the relaxation is insensitive to a sufficiently small perturbation of the constraints. Specifically, we construct an instance of UNIQUE GAMES with k… (More)

- Sushant Sachdeva, Rishi Saket
- 2013 IEEE Conference on Computational Complexity
- 2013

This work studies the inapproximability of two well-known scheduling problems: Concurrent Open Shop and the Assembly Line problem. For both these problems, Bansal and Khot [1] obtained tight (2 - ε)-factor inapproximability, assuming the Unique Games Conjecture (UGC). In this paper, we prove optimal (2 - ε)-factor NP-hardness of approximation… (More)

- Venkatesan Guruswami, Prasad Raghavendra, Rishi Saket, Yi Wu
- Electronic Colloquium on Computational Complexity
- 2010

The Unique Games Conjecture (UGC) has emerged in recent years as the starting point for several optimal inapproximability results. While for <i>none</i> of these results a reverse reduction to Unique Games is known, the assumption of bijective projections in the Label Cover instance nevertheless seems critical in these proofs. In this work, we bypass the… (More)

- Subhash Khot, Rishi Saket
- 21st Annual IEEE Conference on Computational…
- 2006

We study a very basic open problem regarding the PCP characterization of NP, namely, the power of PCPs with 3 non-adaptive queries and perfect completeness. The lowest soundness known till now for such a PCP is 6/8 + epsi given by a construction of Hastad (1997). However, Zwick (1998) shows that a 3-query non-adaptive PCP with perfect completeness cannot… (More)