Related papers: An efficient search strategy for hidden ideals in …
We study the integration of machine learning advice to improve upon traditional data structure designed for efficient search queries. Although there has been recent effort in improving the performance of binary search trees using machine…
Suppose $P_n=\{1,2,...,n\}$ is a partially ordered set with the partial order defined by divisibility, that is, for any two distinct elements $i,j\in P_n$ satisfying $i$ divides $j$, $i<_{P_n} j$. A table $A_n=\{a_i|i=1,2,...,n\}$ of…
We study Matching and other related problems in a partial information setting where the agents' utilities for being matched to other agents are hidden and the mechanism only has access to ordinal preference information. Our model is…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
In this paper, we present a method using AI techniques to solve a case of pure mathematics applications for finding narrow admissible tuples. The original problem is formulated into a combinatorial optimization problem. In particular, we…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
We consider the problem where P is an unknown permutation on {0,1,...,2^n - 1}, y is an element of {0,1,...,2^n - 1}, and the goal is to determine the minimum r > 0 such that P^r(y) = y (where P^r is P composed with itself r times).…
We study the space requirement of $m$-ary search trees under the random permutation model when $m \geq 27$ is fixed. Chauvin and Pouyanne have shown recently that $X_n$, the space requirement of an $m$-ary search tree on $n$ keys, equals…
We study the number of distance queries needed to identify certain properties of a hidden tree $T$ on $n$ vertices. A distance query consists of two vertices $x,y$, and the answer is the distance of $x$ and $y$ in $T$. We determine the…
We present a novel LLM-informed model-based planning framework, and a novel prompt selection method, for object search in partially-known environments. Our approach uses an LLM to estimate statistics about the likelihood of finding the…
We study the problem of learning a good search policy for combinatorial search spaces. We propose retrospective imitation learning, which, after initial training by an expert, improves itself by learning from \textit{retrospective…
We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…
We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider…
In this work, we define the problem of finding an optimal query plan as finding spanning trees with low costs. This approach empowers the utilization of a series of spanning tree algorithms, thereby enabling systematic exploration of the…
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 study protected nodes in $m$-ary search trees, by putting them in context of generalised P\'olya urns. We show that the number of two-protected nodes (the nodes that are neither leaves nor parents of leaves) in a random ternary search…
Some astronomy projects require a blind search through a vast number of hypotheses to detect objects of interest. The number of hypotheses to test can be in the billions. A naive blind search over every single hypothesis would be far too…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
We give an efficient algorithm to enumerate all elements of a Pareto front in a multi-objective optimization problem in which the space of values is finite for all objectives. Our algorithm uses a feasibility check for a search space…
We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of $n$ data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the…