Related papers: A Simple Search Problem
Chaitin's work, in its depth and breadth, encompasses many areas of scientific and philosophical interest. It helped establish the accepted mathematical concept of randomness, which in turn is the basis of tools that I have developed to…
The paper is a second in a series of two papers evaluating the power of a new scheme that generates search heuristics mechanically. The heuristics are extracted from an approximation scheme called mini-bucket elimination that was recently…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
The Santa Claus problem is a fundamental problem in fair division: the goal is to partition a set of heterogeneous items among heterogeneous agents so as to maximize the minimum value of items received by any agent. In this paper, we study…
In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning…
We define the parametric closure problem, in which the input is a partially ordered set whose elements have linearly varying weights and the goal is to compute the sequence of minimum-weight lower sets of the partial order as the weights…
Cognitive science and theoretical computer science both seek to classify and explain the difficulty of tasks. Mechanisms of intelligence are those that reduce task difficulty. Here we map concepts from the computational complexity of a…
Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…
We consider an agent seeking to obtain an item, potentially available at different locations in a physical environment. The traveling costs between locations are known in advance, but there is only probabilistic knowledge regarding the…
We address prehensile pushing, the problem of manipulating a grasped object by pushing against the environment. Our solution is an efficient nonlinear trajectory optimization problem relaxed from an exact mixed integer non-linear trajectory…
Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the…
In this paper, we consider the minimum spanning tree problem (for short, MSTP) on an arbitrary set of $n$ points of $d$-dimensional space in $l_1$-norm. For this problem, for each fixed $d\geq 2$, there is a known algorithm of the…
Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…
In the bin covering problem, the goal is to fill as many bins as possible up to a certain minimal level with a given set of items of different sizes. Online variants, in which the items arrive one after another and have to be packed…
One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…
The Pandora's box problem (Weitzman 1979) is a core model in economic theory that captures an agent's (Pandora's) search for the best alternative (box). We study an important generalization of the problem where the agent can either fully…
We consider the Ordered Open End Bin Packing problem. Items of sizes in $(0,1]$ are presented one by one, to be assigned to bins in this order. An item can be assigned to any bin for which the current total size strictly below $1$. This…
We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…
Recent numerical results show that non-Bayesian knowledge revision may be helpful in search engine training and optimization. In order to demonstrate how basic assumption about about the physical nature (and hence the observed statistics)…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…