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The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k and their adjacent edges are removed until no vertices of degree less than k are left. Often the question is whether the remaining hypergraph, the k-core, is empty or not. In some settings, it may be possible to remove either vertices or edges from the hypergraph before peeling, at some cost. For example, in hashing applications where keys correspond to edges and buckets to vertices, one might use an additional side data structure, commonly referred to as a stash, to separately handle some keys in order to avoid collisions. The natural question in such cases is to find the minimum number of edges (or vertices) that need to be stashed in order to realize an empty k-core. We show that both these problems are NP-complete for all $k geq 2$ on graphs and regular hypergraphs, with the sole exception being that the edge variant of stashing is solvable in polynomial time for $k = 2$ on standard (2-uniform) graphs.
We consider the complexity properties of modern puzzle games, Hexiom, Cut the Rope and Back to Bed. The complexity of games plays an important role in the type of experience they provide to players. Back to Bed is shown to be PSPACE-Hard and the firs
We study the problem of approximating the value of a Unique Game instance in the streaming model. A simple count of the number of constraints divided by $p$, the alphabet size of the Unique Game, gives a trivial $p$-approximation that can be computed
The Earth Mover Distance (EMD) between two sets of points $A, B subseteq mathbb{R}^d$ with $|A| = |B|$ is the minimum total Euclidean distance of any perfect matching between $A$ and $B$. One of its generalizations is asymmetric EMD, which is the min
We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable Boolean CSPs
In this work, we show the first worst-case to average-case reduction for the classical $k$-SUM problem. A $k$-SUM instance is a collection of $m$ integers, and the goal of the $k$-SUM problem is to find a subset of $k$ elements that sums to $0$. In t