Related papers: Challenges in computational lower bounds
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
We present deterministic techniques for computing upper and lower bounds on marginal probabilities in sigmoid and noisy-OR networks. These techniques become useful when the size of the network (or clique size) precludes exact computations.…
This paper studies the problem of computing quasi-upward planar drawings of bimodal plane digraphs with minimum curve complexity, i.e., drawings such that the maximum number of bends per edge is minimized. We prove that every bimodal plane…
We describe a convex programming approach to the calculation of lower bounds on the minimum cost of constrained decentralized control problems with nonclassical information structures. The class of problems we consider entail the…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
We study weakest precondition reasoning about the (co)variance of outcomes and the variance of run-times of probabilistic programs with conditioning. For outcomes, we show that approximating (co)variances is computationally more difficult…
A significant amount of recent research work has addressed the problem of solving various data management problems in the cloud. The major algorithmic challenges in map-reduce computations involve balancing a multitude of factors such as…
We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and…
Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…
We address two sets of long-standing open questions in probability theory, from a computational complexity perspective: divisibility of stochastic maps, and divisibility and decomposability of probability distributions. We prove that finite…
We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the latter…
In this chapter, we will first present the most standard computational challenges met in Bayesian Statistics, focussing primarily on mixture estimation and on model choice issues, and then relate these problems with computational solutions.…
We consider the problem of finding lower bounds on the I/O complexity of arbitrary computations in a two level memory hierarchy. Executions of complex computations can be formalized as an evaluation order over the underlying computation…
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We present here algorithms for efficient computation of linear algebra problems over finite fields.
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…
We consider the problem of succinctly encoding a static map to support approximate queries. We derive upper and lower bounds on the space requirements in terms of the error rate and the entropy of the distribution of values over keys: our…