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Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources…
In this article we propose a heuristic algorithm to explore search space trees associated with instances of combinatorial optimization problems. The algorithm is based on Monte Carlo tree search, a popular algorithm in game playing that is…
We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…
This paper investigates the optimal signal detection problem with a particular interest in large-scale multiple-input multiple-output (MIMO) systems. The problem is NP-hard and can be solved optimally by searching the shortest path on the…
Designing search algorithms for finding global optima is one of the most active research fields, recently. These algorithms consist of two main categories, i.e., classic mathematical and metaheuristic algorithms. This article proposes a…
The personnel rostering problem is the problem of finding an optimal way to assign employees to shifts, subject to a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative…
Document retrieval is one of the best established information retrieval activities since the sixties, pervading all search engines. Its aim is to obtain, from a collection of text documents, those most relevant to a pattern query. Current…
Innovative shared mobility services provide on-demand flexible mobility options and have the potential to alleviate traffic congestion. These attractive services are challenging from different perspectives. One major challenge in such…
While modern biotechnologies allow synthesizing new proteins and function measurements at scale, efficiently exploring a protein sequence space and engineering it remains a daunting task due to the vast sequence space of any given protein.…
Beam search is a go-to strategy for decoding neural sequence models. The algorithm can naturally be viewed as a subset optimization problem, albeit one where the corresponding set function does not reflect interactions between candidates.…
The growing popularity of generative language models has amplified interest in interactive methods to guide model outputs. Prompt refinement is considered one of the most effective means to influence output among these methods. We identify…
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…
Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known…
Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
We introduce an adaptive tree search algorithm, that can find high-scoring outputs under translation models that make no assumptions about the form or structure of the search objective. This algorithm -- a deterministic variant of Monte…
Algorithms for efficiently finding optimal alphabetic decision trees -- such as the Hu-Tucker algorithm -- are well established and commonly used. However, such algorithms generally assume that the cost per decision is uniform and thus…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
This paper studies the performances of BERT combined with tree structure in short sentence ranking task. In retrieval-based question answering system, we retrieve the most similar question of the query question by ranking all the questions…
We study the dynamic optimality conjecture, which predicts that splay trees are a form of universally efficient binary search tree, for any access sequence. We reduce this claim to a regular access bound, which seems plausible and might be…