Related papers: Bloom maps
In order to find out the limiting speed of solving a specific problem using computer, this essay provides a method based on information entropy. The relationship between the minimum computational complexity and information entropy change is…
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…
Information inequalities appear in many database applications such as query output size bounds, query containment, and implication between data dependencies. Recently Khamis et al. proposed to study the algorithmic aspects of information…
We consider the \emph{two-dimensional range maximum query (2D-RMQ)} problem: given an array $A$ of ordered values, to pre-process it so that we can find the position of the smallest element in the sub-matrix defined by a (user-specified)…
A filter is a widely used data structure for storing an approximation of a given set $S$ of elements from some universe $U$ (a countable set).It represents a superset $S'\supseteq S$ that is ''close to $S$'' in the sense that for $x\not\in…
We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…
Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
Bloom filters are widely used data structures that compactly represent sets of elements. Querying a Bloom filter reveals if an element is not included in the underlying set or is included with a certain error rate. This membership testing…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
Establishing bounds on the accuracy achievable by localization techniques represents a fundamental technical issue. Bounds on localization accuracy have been derived for cases in which the position of an agent is estimated on the basis of a…
In this paper, we study the form over the minimum spanning tree problem (MST) from which we will derive an intuitively generalized model and new methods with the upper bound of runtimes of logarithm. The new pattern we made has taken…
Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we presented sub-tree based upper and lower bounds on the partition…
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
Constraints on entropies are considered to be the laws of information theory. Even though the pursuit of their discovery has been a central theme of research in information theory, the algorithmic aspects of constraints on entropies remain…
Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…
The Bandwidth Problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel…
Rooted trees with probabilities are used to analyze properties of a variable length code. A bound is derived on the difference between the entropy rates of the code and a memoryless source. The bound is in terms of normalized informational…