Related papers: Unifying and Strengthening Hardness for Dynamic Pr…
We study online robust matrix completion on graphs. At each iteration a vector with some entries missing is revealed and our goal is to reconstruct it by identifying the underlying low-dimensional subspace from which the vectors are drawn.…
We present the first truly subcubic, combinatorial algorithm for detecting an induced $4$-cycle in a graph. The running time is $O(n^{2.84})$ on $n$-node graphs, thus separating the task of detecting induced $4$-cycles from detecting…
We study the binary perceptron, a random constraint satisfaction problem that asks to find a Boolean vector in the intersection of independently chosen random halfspaces. A striking feature of this model is that at every positive constraint…
There has been a resurgence of interest in lower bounds whose truth rests on the conjectured hardness of well known computational problems. These conditional lower bounds have become important and popular due to the painfully slow progress…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
We study the problem of detecting outlier pairs of strongly correlated variables among a collection of $n$ variables with otherwise weak pairwise correlations. After normalization, this task amounts to the geometric task where we are given…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph $G$ such that we may support insertions and deletions of edges in $G$ as well as distance queries between any two nodes $u,v$ subject to the constraint…
We propose a general method for combinatorial online learning problems whose offline optimization problem can be solved efficiently via a dynamic programming algorithm defined by an arbitrary min-sum recurrence. Examples include online…
We study the problem of finding elements in the intersection of an arbitrary conic variety in $\mathbb{F}^n$ with a given linear subspace (where $\mathbb{F}$ can be the real or complex field). This problem captures a rich family of…
A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\sum_{ij\in E} C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
It is known that the multiplication of an $N \times M$ matrix with an $M \times P$ matrix can be performed using fewer multiplications than what the naive $NMP$ approach suggests. The most famous instance of this is Strassen's algorithm for…
Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with $n$ labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game,…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
In this paper we show that every combinatorial problem has an exact explicit equation that returns its solution. We present a method to obtain an equation that solves exactly any combinatorial problem, both inversion, constraint…
In 2010, P\v{a}tra\c{s}cu proposed the following three-phase dynamic problem, as a candidate for proving polynomial lower bounds on the operational time of dynamic data structures: I: Preprocess a collection of sets $\vec{S} = S_1, \ldots ,…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in…