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- Tracy Grauman, Stephen G. Hartke, +5 authors Hehui Wu
- Inf. Process. Lett.
- 2008

A hub set in a graph G is a set U ⊆ V (G) such that any two vertices outside U are connected by a path whose internal vertices lie in U. We prove that h(G) ≤ h c (G) ≤ γ c (G) ≤ h(G) + 1, where h(G), h c (G), and γ c (G), respectively, are the minimum sizes of a hub set in G, a hub set inducing a connected subgraph, and a connected dominating set.… (More)

- Marieke Huisman, Pratik Worah, Kim Sunesen
- 19th IEEE Computer Security Foundations Workshop…
- 2006

This paper studies observational determinism, a generalisation of non-interference for multi-threaded programs. Standard notions of non-interference only consider input and output of programs, but to ensure the security of multithreaded programs, one has to consider execution traces. In earlier work, Zdancewic and Myers propose to consider a multi-threaded… (More)

- Jeff Erickson, Pratik Worah
- Discrete & Computational Geometry
- 2010

An essential cycle on a surface is a simple cycle that cannot be continuously deformed to a point or a single boundary. We describe algorithms to compute the shortest essential cycle in an orientable combinatorial surface in O(n 2 log n) time, or in O(n log n) time when both the genus and number of boundaries are fixed. Our results correct an error in a… (More)

- Erin W. Chambers, Jeff Erickson, Pratik Worah
- Symposium on Computational Geometry
- 2008

The (Vietoris-)Rips complex of a discrete point-set <i>P</i> is an abstract simplicial complex in which a subset of <i>P</i> defines a simplex if and only if the diameter of that subset is at most 1. We describe an efficient algorithm to determine whether a given cycle in a planar Rips complex is contractible. Our algorithm requires <i>O</i>(<i>m</i> log… (More)

- Madhur Tulsiani, Pratik Worah
- 2013 IEEE Conference on Computational Complexity
- 2012

We consider the complexity of LS<sub>+</sub> refutations of unsatisfiable instances of Constraint Satisfaction Problems (k-CSPs) when the underlying predicate supports a pairwise independent distribution on its satisfying assignments. This is the most general condition on the predicates under which the corresponding MAX k-CSP problem is known to be… (More)

- Subhash Khot, Madhur Tulsiani, Pratik Worah
- STOC
- 2013

For a predicate <i>f</i>: {-1, 1}<sup><i>k</i></sup> ↦ {0, 1} with <i>ρ</i>(<i>f</i>) = |<i>f</i><sup>-1</sup>(1)|/2<sup><i>k</i></sup>, we call the predicate <i>strongly approximation resistant</i> if given a near-satisfiable instance of CSP(<i>f</i>), it is computationally <i>hard</i> to find an assignment such that the fraction of constraints… (More)

- Timothy D. LeSaulnier, Noah Prince, Paul S. Wenger, Douglas B. West, Pratik Worah
- SIAM J. Discrete Math.
- 2013

Let G be a weighted graph in which each vertex initially has weight 1. A total acquisition move transfers all the weight from a vertex u to a neighboring vertex v, under the condition that before the move the weight on v is at least as large as the weight on u. The (total) acquisition number of G, written a t (G), is the minimum size of the set of vertices… (More)

- Gurashish Singh Brar, Susmit Biswas, Sudipta Kundu, Arijit Mukhopadhyay, Pratik Worah, Anupam Basu
- VLSI Design
- 2004

Portable and affordable assistive devices are calling necessities for the physically challenged population putting forth the requirement of designing embedded systems tuned to specific assistive applications. In this paper, we present a low footprint embedded operating system, OaSis, which forms the core of embedded devices being developed for the speech… (More)

- Subhash Khot, Madhur Tulsiani, Pratik Worah
- ICALP
- 2012

A boolean predicate f : {0, 1} → {0, 1} is said to be somewhat approximation resistant if for some constant τ > |f −1(1)| 2k , given a τ -satisfiable instance of the MAX k-CSP(f) problem, it is NP-hard to find an assignment that strictly beats the naive algorithm that outputs a uniformly random assignment. Let τ(f) denote the supremum over all τ for which… (More)

- Pratik Worah
- J. Comb. Optim.
- 2012

Lovász and Schrijver [17] introduced several lift and project methods for 0-1 integer programs, now collectively known as Lovász-Schrijver (LS) hierarchies. Several lower bounds have since been proven for the rank of various linear programming relaxations in the LS and LS+ hierarchies. In this paper we investigate rank bounds in the more general LS∗… (More)