Sairam Subramanian

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We give a linear-time algorithm for single-source shortest paths in planar graphs with nonnegative edge-lengths. Our algorithm also yields a linear-time algorithm for maximum flow in a planar graph with the source and sink on the same face. For the case where negative edge-lengths are allowed, we give an algorithm requiring O(n 3 log(nL)) time, where L is(More)
1 Introduction and motivation External 2-dimensional range searching is a fundamental problem with many applications in relational, object-oriented, spatial, and temporal databases. For example, interval intersection can be reduced to 2-sided, 2-dimensional searching and indexing class hierarchies of objects to 3-sided, 2-dimensional searching. In this(More)
External 2-dimensional searching is a fundamental problem with many applications in relational, object-oriented, spatial, and temporal databases. For example, interval intersection can be reduced to 2-sided, 2-dimensional searching and indexing class hierarchies of objects to 3-sided, 2-dimensional searching. <italic>Path caching</italic> is a new technique(More)
Molecular automata that combine sensing, computation and actuation enable programmable manipulation of biological systems. We use RNA interference (RNAi) in human kidney cells to construct a molecular computing core that implements general Boolean logic to make decisions based on endogenous molecular inputs. The state of an endogenous input is encoded by(More)
We present a new complexity theoretic approach to incremental computation. We de ne complexity classes that capture the intuitive notion of incremental e ciency and study their relation to existing complexity classes. We show that problems that have small sequential space complexity also have small incremental time complexity. We show that all common(More)
We develop order bounds on the refresh rate of computing functions over large multi-hop sensor networks, with finite degree (finite neighbors for each node). The refresh rate quantifies how often the function can be re-computed with new data at sensor nodes. Giridhar and Kumar (2005) considered deterministic function computation for two important classes of(More)
We give a randomized parallel algorithm for computing single-source shortest paths in weighted digraphs. We show that the exact shortest-path problem can be efficiently reduced to solving a series of approximate shortest-path subproblems. Our algorithm for the approximate shortest-path problem is based on the technique used by Ullman and Yannakakis in a(More)
Synthetic biology efforts have largely focused on small engineered gene networks, yet understanding how to integrate multiple synthetic modules and interface them with endogenous pathways remains a challenge. Here we present the design, system integration, and analysis of several large scale synthetic gene circuits for artificial tissue homeostasis.(More)
In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter $\epsilon$ such that $0<\epsilon$ , our algorithm maintains approximate all-pairs shortest paths in an undirected planar graph G with nonnegative edge lengths. The approximate paths are guaranteed to be accurate to(More)