We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing, we fix the function and then vary the underlying network topology. This complements the recent ... more >>>
A $k$-uniform hypergraph $G$ of size $n$ is said to be $\varepsilon$-far from having an independent set of size $\rho n$ if one must remove at least $\varepsilon n^k$ edges of $G$ in order for the remaining hypergraph to have an independent set of size $\rho n$. In this work, ... more >>>
We design a $0.795$ approximation algorithm for the Max-Bisection problem
restricted to regular graphs. In the case of three regular graphs our
results imply an approximation ratio of $0.834$.
We analyze the addition of a simple local improvement step to various known
randomized approximation algorithms.
Let $\alpha \simeq 0.87856$ denote the best approximation ratio currently
known for the Max Cut problem on general graphs~\cite{GW95}.
We consider a semidefinite relaxation of the Max Cut problem,
round it using the ...
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