Related papers: Estimating Total Search Space Size for Specific Pi…
We consider uniformly random set partitions of size $n$ with exactly $k$ blocks, and uniformly random permutations of size $n$ with exactly $k$ cycles, under the regime where $n-k \sim t\sqrt{n}$, $t>0$. In this regime, there is a simple…
We consider generalizations of the familiar fifteen-piece sliding puzzle on the 4 by 4 square grid. On larger grids with more pieces and more holes, asymptotically how fast can we move the puzzle into the solved state? We also give a…
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 prove that chess played on the infinite chessboard $\mathbb{Z}^2$ with infinitely many pieces is as powerful as it could possibly be, by showing that every open Gale-Stewart game with draws is strategically equivalent to some infinite…
We propose Expected Work Search (EWS), a new game solving algorithm. EWS combines win rate estimation, as used in Monte Carlo Tree Search, with proof size estimation, as used in Proof Number Search. The search efficiency of EWS stems from…
We study the compositions of an integer n whose part sizes do not exceed a fixed integer k. We use the methods of analytic combinatorics to obtain precise asymptotic formulas for the number of such compositions, the total number of parts…
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…
Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed…
A quantitative method is described for comparing chess openings. Test openings and baseline openings are run through chess engines under controlled conditions and compared to evaluate the effectiveness of the test openings. The results are…
Equilibria of realistic multiplayer games constitute a key solution concept both in practical applications, such as online advertising auctions and electricity markets, and in analytical frameworks used to study strategic voting in…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
We prove PSPACE-completeness of two classic types of Chess problems when generalized to n-by-n boards. A "retrograde" problem asks whether it is possible for a position to be reached from a natural starting position, i.e., whether the…
Predicting the relative value of any given chess piece in a position remains an open challenge, as a piece's contribution depends on its spatial relationships with every other piece on the board. We demonstrate that incorporating the state…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
This paper introduces a novel algorithm for two-player deterministic games with perfect information, which we call PROBS (Predict Results of Beam Search). Unlike existing methods that predominantly rely on Monte Carlo Tree Search (MCTS) for…
We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…
Concurrent games with a fixed number of agents have been thoroughly studied, with various solution concepts and objectives for the agents. In this paper, we consider concurrent games with an arbitrary number of agents, and study the problem…
When shuffling a deck of cards, one probably wants to make sure it is thoroughly shuffled. A way to do this is by sifting through the cards to ensure that no adjacent cards are the same number, because surely this is a poorly shuffled deck.…
We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm…