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We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…
This paper describes in detail the bitonic sort algorithm,and implements the bitonic sort algorithm based on cuda architecture.At the same time,we conduct two effective optimization of implementation details according to the characteristics…
Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can…
Game solving is the process of finding the theoretical outcome for a game, assuming that all player choices are optimal. This paper focuses on a technique that can reduce the heuristic search space significantly for 7x7 Killall-Go. In Go…
Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…
An analysis of the average-case complexity of solving random 3-Satisfiability (SAT) instances with backtrack algorithms is presented. We first interpret previous rigorous works in a unifying framework based on the statistical physics…
We present a novel method for solving square jigsaw puzzles based on global optimization. The method is fully automatic, assumes no prior information, and can handle puzzles with known or unknown piece orientation. At the core of the…
Heuristic algorithms such as simulated annealing, Concorde, and METIS are effective and widely used approaches to find solutions to combinatorial optimization problems. However, they are limited by the high sample complexity required to…
Tetris Block Puzzle is a single player stochastic puzzle in which a player places blocks on an 8 x 8 grid to complete lines; its popular variants have amassed tens of millions of downloads. Despite this reach, there is little principled…
Fifteen Puzzle problem is one of the most classical problems that have captivated mathematical enthusiasts for centuries. This is mainly because of the huge size of the state space with approximately 1013 states that have to be explored and…
When combined properly, search techniques can reveal the full potential of sophisticated branching heuristics. We demonstrate this observation on the well-known class of random 3-SAT formulae. First, a new branching heuristic is presented,…
We determine the complexity of several constraint satisfaction problems using the heuristic algorithm, WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models…
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…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…
The aim of this paper is twofold. First, we introduce "resource constraints" as a general concept that covers many practical restrictions on experimental design. Second, for computing efficient exact designs of experiments under any…
There are currently two philosophies for building grammars and parsers -- Statistically induced grammars and Wide-coverage grammars. One way to combine the strengths of both approaches is to have a wide-coverage grammar with a heuristic…
We describe and evaluate the algorithmic techniques that are used in the FF planning system. Like the HSP system, FF relies on forward state space search, using a heuristic that estimates goal distances by ignoring delete lists. Unlike…
Discrete optimization problems often arise in deep learning tasks, despite the fact that neural networks typically operate on continuous data. One class of these problems involve objective functions which depend on neural networks, but…
The vertex coloring problem is a well-known NP-hard problem and has many applications in operations research and in scheduling. A conventional approach to the problem solves the k-colorability problem iteratively, decreasing k one by one.…
Most optimization problems in real life applications are often highly nonlinear. Local optimization algorithms do not give the desired performance. So, only global optimization algorithms should be used to obtain optimal solutions. This…