Related papers: Crossing the Logarithmic Barrier for Dynamic Boole…
In the decision tree computation model for Boolean functions, the depth corresponds to query complexity, and size corresponds to storage space. The depth measure is the most well-studied one, and is known to be polynomially related to…
Dynamic optimization problems involving discrete decisions have several applications, yet lead to challenging optimization problems that must be addressed efficiently. Combining discrete variables with potentially nonlinear constraints…
Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems. A prominent approach is to characterize the limits of restricted models of…
This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing $\tilde{\Omega}(n^2)$ lower bounds for cornerstone problems,…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…
A dictionary data structure maintains a set of at most $n$ keys from the universe $[U]$ under key insertions and deletions, such that given a query $x \in [U]$, it returns if $x$ is in the set. Some variants also store values associated to…
We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…
We give upper and lower bounds on the power of subsystems of the Ideal Proof System (IPS), the algebraic proof system recently proposed by Grochow and Pitassi, where the circuits comprising the proof come from various restricted algebraic…
We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…
We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…
In this paper, we study the problem of minimizing a polynomial function with literals over all binary points, often referred to as pseudo-Boolean optimization. We investigate the fundamental limits of computation for this problem by…
Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision…
Minimal models of a Boolean formula play a pivotal role in various reasoning tasks. While previous research has primarily focused on qualitative analysis over minimal models; our study concentrates on the quantitative aspect, specifically…
In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In…
This paper discovers that the neural network with lower decision boundary (DB) variability has better generalizability. Two new notions, algorithm DB variability and $(\epsilon, \eta)$-data DB variability, are proposed to measure the…
We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…
Roughgarden, Vassilvitskii, and Wang (JACM 18) recently introduced a novel framework for proving lower bounds for Massively Parallel Computation using techniques from boolean function complexity. We extend their framework in two different…
We introduce lower-bound certificates for classical planning tasks, which can be used to prove the unsolvability of a task or the optimality of a plan in a way that can be verified by an independent third party. We describe a general…
We consider the problem of digitalizing Euclidean segments. Specifically, we look for a constructive method to connect any two points in $\mathbb{Z}^d$. The construction must be {\em consistent} (that is, satisfy the natural extension of…
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…