Related papers: Tight Analyses of Ordered and Unordered Linear Pro…
In this paper, we give new, tight subexponential lower bounds for a number of graph embedding problems. We introduce two related combinatorial problems, which we call String Crafting and Orthogonal Vector crafting, and show that these…
Linear predictors form a rich class of hypotheses used in a variety of learning algorithms. We present a tight analysis of the empirical Rademacher complexity of the family of linear hypothesis classes with weight vectors bounded in…
A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend Omega(log log n / log log log n) amortized time on the decrease-key operation (given O(log n) amortized-time…
These lecture notes show that linear probing takes expected constant time if the hash function is 5-independent. This result was first proved by Pagh et al. [STOC'07,SICOMP'09]. The simple proof here is essentially taken from [Patrascu and…
We present a new threshold phenomenon in data structure lower bounds where slightly reduced update times lead to exploding query times. Consider incremental connectivity, letting t_u be the time to insert an edge and t_q be the query time.…
We prove that hashing $n$ balls into $n$ bins via a random matrix over $\mathbf{F}_2$ yields expected maximum load $O(\log n / \log \log n)$. This matches the expected maximum load of a fully random function and resolves an open question…
Formal reasoning about the time complexity of algorithms and data structures is usually done in interactive theorem provers like Isabelle/HOL. This includes reasoning about amortized time complexity which looks at the worst case performance…
Can we analyze data without decompressing it? As our data keeps growing, understanding the time complexity of problems on compressed inputs, rather than in convenient uncompressed forms, becomes more and more relevant. Suppose we are given…
Hashing with linear probing dates back to the 1950s, and is among the most studied algorithms. In recent years it has become one of the most important hash table organizations since it uses the cache of modern computers very well.…
The System of Linear Equations Problem (SLEP) is specified by a complex invertible matrix $A$, the condition number $\kappa$ of $A$, a vector $b$, a Hermitian matrix $M$ and an accuracy $\epsilon$, and the task is to estimate $x^\dagger…
This paper studies algorithmic meta theorems for property testing with \emph{constant running time} in the bounded degree model. In (Adler, Harwath 2018) it was shown that on graph classes $\mathcal C^{w}_d$ consisting of all graphs with…
We consider a monotone submodular maximization problem whose constraint is described by a logic formula on a graph. Formally, we prove the following three `algorithmic metatheorems.' (1) If the constraint is specified by a monadic…
Temporal graphs are introduced to model systems where the relationships among the entities of the system evolve over time. In this paper, we consider the temporal graphs where the edge set changes with time and all the changes are known a…
We revisit the \emph{leaderboard problem} introduced by Blum and Hardt (2015) in an effort to reduce overfitting in machine learning benchmarks. We show that a randomized version of their Ladder algorithm achieves leaderboard error…
High-dimensional data analysis using traditional models suffers from overparameterization. Two types of techniques are commonly used to reduce the number of parameters - regularization and dimension reduction. In this project, we combine…
We present algorithms that run in linear time on pointer machines for a collection of problems, each of which either directly or indirectly requires the evaluation of a function defined on paths in a tree. These problems previously had…
We consider a classical scheduling problem on $m$ identical machines. For an arbitrary constant $q>1$, the aim is to assign jobs to machines such that $\sum_{i=1}^m C_i^q$ is minimized, where $C_i$ is the total processing time of jobs…
The list-labeling problem captures the basic task of storing a dynamically changing set of up to $n$ elements in sorted order in an array of size $m = (1 + \Theta(1))n$. The goal is to support insertions and deletions while moving around…
The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the…
Despite significant progress in the theory of evolutionary algorithms, the theoretical understanding of evolutionary algorithms which use non-trivial populations remains challenging and only few rigorous results exist. Already for the most…