Related papers: Nearly Optimal Minimax Tree Search?
We introduce a search game for two players played on a "scenario" consisting of a ground set together with a collection of feasible partitions. This general setting allows us to obtain new characterisations of many width parameters such as…
We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…
$\Theta_6$-Graphs graphs are important geometric graphs that have many applications especially in wireless sensor networks. They are equivalent to Delaunay graphs where empty equilateral triangles take the place of empty circles. We…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…
Computing lower and upper bounds on the competitive ratio of online algorithms is a challenging question: For a minimization combinatorial problem, proving a competitive ratio for a given algorithm leads to an upper bound. However computing…
Lookahead search is perhaps the most natural and widely used game playing strategy. Given the practical importance of the method, the aim of this paper is to provide a theoretical performance examination of lookahead search in a wide…
Monte Carlo Tree Search (MCTS), most famously used in game-play artificial intelligence (e.g., the game of Go), is a well-known strategy for constructing approximate solutions to sequential decision problems. Its primary innovation is the…
We show optimal lower bounds for spanning forest computation in two different models: * One wants a data structure for fully dynamic spanning forest in which updates can insert or delete edges amongst a base set of $n$ vertices. The sole…
Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. The expanding search problem asks for a search sequence of the vertices so as to minimize the expected time for…
The Minimum Vertex Cover (MinVC) problem is a well-known NP-hard problem. Recently there has been great interest in solving this problem on real-world massive graphs. For such graphs, local search is a promising approach to finding optimal…
Optimization of searching the best possible action depending on various states like state of environment, system goal etc. has been a major area of study in computer systems. In any search algorithm, searching best possible solution from…
Tree-decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. The main property of tree-decompositions is the width (the maximum size of a bag minus 1). We show that every graph has a…
We consider the problem of exploring an unknown tree with a team of $k$ initially colocated mobile agents. Each agent has limited energy and cannot, as a result, traverse more than $B$ edges. The goal is to maximize the number of nodes…
A classical result of Koml\'os, S\'ark\"ozy and Szemer\'edi states that every $n$-vertex graph with minimum degree at least $(1/2+ o(1))n$ contains every $n$-vertex tree with maximum degree $O(n/\log{n})$ as a subgraph, and the bounds on…
Graph-based algorithms have demonstrated state-of-the-art performance in the nearest neighbor search (NN-Search) problem. These empirical successes urge the need for theoretical results that guarantee the search quality and efficiency of…
The segment number of a planar graph $G$ is the smallest number of line segments needed for a planar straight-line drawing of $G$. Dujmovi\'c, Eppstein, Suderman, and Wood [CGTA'07] introduced this measure for the visual complexity of…
Finding optimal evolutionary trees from sequence data is typically an intractable problem, and there is usually no way of knowing how close to optimal the best tree from some search truly is. The problem would seem to be particularly acute…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Treewidth is an important structural graph parameter that quantifies how closely a graph resembles a tree-like structure. It has applications in many algorithmic and combinatorial problems. In this paper, we study the treewidth of outer…
We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a…