A star graph is a tree of diameter at most two. A star forest is a graph that consists of node-di... more A star graph is a tree of diameter at most two. A star forest is a graph that consists of node-disjoint star graphs. In the spanning star forest problem, given an unweighted graph G, the objective is to find a star forest that contains all the vertices of G and has the maximum number of edges. This problem is the complement of the dominating set problem in the following sense: On a graph with n vertices, the size of the maximum spanning star forest is equal to n minus the size of the minimum dominating set. We present a 0.71-approximation algorithm for this problem, improving upon the approximation factor of 0.6 of Nguyen et al. [9]. We also present a 0.64-approximation algorithm for the problem on node-weighted graphs. Finally, we present improved hardness of approximation results for the weighted versions of the problem.
We present error-correcting codes that achieve the information-theoretically best possible trade-... more We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every 0 < R < 1 and ε > 0, we present an explicit construction of error-correcting codes of rate R that can be list decoded in polynomial time up to a fraction (1 − R − ε) of worst-case errors. At least theoretically, this meets one of the central challenges in algorithmic coding theory.
The architecture of the modern Internet encompasses a large number of principles, concepts and as... more The architecture of the modern Internet encompasses a large number of principles, concepts and assumptions, that have evolved over several decades. In this paper, we argue that while the current architecture houses an effective design, it is not itself effective in enabling evolution. To achieve the latter goal, we introduce the SILO architecture, a meta-design framework within which the system design can change and evolve. We list some insights about architectural research that guided our work, and also state the goals we formulated for our architecture. We then describe that actual architecture itself, connecting it with relevant prior and current research work. We show how the promise of enabling change is validated by showing our recent work on supporting virtualization as well as cross-layer research in optics using SILO. We present an early case study on the usefulness of SILO in lowering the barrier to contribution and innovation in network protocols, and we conclude with a list of open research problems.
A star graph is a tree of diameter at most two. A star forest is a graph that consists of node-di... more A star graph is a tree of diameter at most two. A star forest is a graph that consists of node-disjoint star graphs. In the spanning star forest problem, given an unweighted graph G, the objective is to find a star forest that contains all the vertices of G and has the maximum number of edges. This problem is the complement of the dominating set problem in the following sense: On a graph with n vertices, the size of the maximum spanning star forest is equal to n minus the size of the minimum dominating set. We present a 0.71-approximation algorithm for this problem, improving upon the approximation factor of 0.6 of Nguyen et al. [9]. We also present a 0.64-approximation algorithm for the problem on node-weighted graphs. Finally, we present improved hardness of approximation results for the weighted versions of the problem.
We present error-correcting codes that achieve the information-theoretically best possible trade-... more We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every 0 < R < 1 and ε > 0, we present an explicit construction of error-correcting codes of rate R that can be list decoded in polynomial time up to a fraction (1 − R − ε) of worst-case errors. At least theoretically, this meets one of the central challenges in algorithmic coding theory.
The architecture of the modern Internet encompasses a large number of principles, concepts and as... more The architecture of the modern Internet encompasses a large number of principles, concepts and assumptions, that have evolved over several decades. In this paper, we argue that while the current architecture houses an effective design, it is not itself effective in enabling evolution. To achieve the latter goal, we introduce the SILO architecture, a meta-design framework within which the system design can change and evolve. We list some insights about architectural research that guided our work, and also state the goals we formulated for our architecture. We then describe that actual architecture itself, connecting it with relevant prior and current research work. We show how the promise of enabling change is validated by showing our recent work on supporting virtualization as well as cross-layer research in optics using SILO. We present an early case study on the usefulness of SILO in lowering the barrier to contribution and innovation in network protocols, and we conclude with a list of open research problems.
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Papers by RUDRA BOX