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Existing clustering algorithms such as K-means often need to preset parameters such as the number of categories K, and such parameters may lead to the failure to output objective and consistent clustering results. This paper introduces a…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
Suppose a language $L$ can be decided by a bounded-error randomized algorithm that runs in space $S$ and time $n \cdot \text{poly}(S)$. We give a randomized algorithm for $L$ that still runs in space $O(S)$ and time $n \cdot \text{poly}(S)$…
Selecting $k$ out of $m$ items based on the preferences of $n$ heterogeneous agents is a widely studied problem in algorithmic game theory. If agents have approval preferences over individual items and harmonic utility functions over…
We show that combining two different hypothetical enhancements to quantum computation---namely, quantum advice and non-collapsing measurements---would let a quantum computer solve any decision problem whatsoever in polynomial time, even…
Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…
A basic goal in complexity theory is to understand the communication complexity of number-on-the-forehead problems $f\colon(\{0,1\}^n)^{k}\to\{0,1\}$ with $k\gg\log n$ parties. We study the problems of inner product and set disjointness and…
There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…
We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…
Let $P:\{0,1\}^k \to \{0,1\}$ be a nontrivial $k$-ary predicate. Consider a random instance of the constraint satisfaction problem $\mathrm{CSP}(P)$ on $n$ variables with $\Delta n$ constraints, each being $P$ applied to $k$ randomly chosen…
Motivated by recent work on scheduling with predicted job sizes, we consider the performance of scheduling algorithms with minimal advice, namely a single bit. Besides demonstrating the power of very limited advice, such schemes are quite…
Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…
Internet supercomputing is an approach to solving partitionable, computation-intensive problems by harnessing the power of a vast number of interconnected computers. This paper presents a new algorithm for the problem of using network…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
For every p in (0,1/2), we give an explicit construction of binary codes of rate approaching "capacity" 1-H(p) that enable reliable communication in the presence of worst-case additive errors}, caused by a channel oblivious to the codeword…
We investigate the question whether Subset Sum can be solved by a polynomial-time algorithm with access to a certificate of length poly(k) where k is the maximal number of bits in an input number. In other words, can it be solved using only…
The solution space of a K-satisfiability (K-SAT) formula is a collection of solution clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips. Knowledge of the statistical…
We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…