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We consider finite range Gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi--invariants, supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
This paper introduces the Partition Tree Weighting technique, an efficient meta-algorithm for piecewise stationary sources. The technique works by performing Bayesian model averaging over a large class of possible partitions of the data…
One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the…
We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…
Retrosynthesis, the process of deconstructing a target molecule into simpler precursors, is crucial for computer-aided synthesis planning (CASP). Widely adopted tree-search methods often suffer from exponential computational complexity. In…
There are various approaches to exploiting "hidden structure" in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure…
We introduce and study a directed analogue of the weighted Tree Augmentation Problem (WTAP). In the weighted Directed Tree Augmentation Problem (WDTAP), we are given an oriented tree $T = (V,A)$ and a set of directed links $L \subseteq V…
`Tree pruning' (TP) is an algorithm for probabilistic inference on binary Markov random fields. It has been recently derived by Dror Weitz and used to construct the first fully polynomial approximation scheme for counting independent sets…
In the longest plane spanning tree problem, we are given a finite planar point set $\mathcal{P}$, and our task is to find a plane (i.e., noncrossing) spanning tree for $\mathcal{P}$ with maximum total Euclidean edge length. Despite more…
We consider the problem of learning decision rules for prediction with feature budget constraint. In particular, we are interested in pruning an ensemble of decision trees to reduce expected feature cost while maintaining high prediction…
A powerful technique for solving combinatorial optimization problems is to reduce the search space without compromising the solution quality by exploring intrinsic mathematical properties of the problems. For the maximum weight independent…
Tree Containment is a fundamental problem in phylogenetics useful for verifying a proposed phylogenetic network, representing the evolutionary history of certain species. Tree Containment asks whether the given phylogenetic tree (for…
Finding the set of leaves for an unbounded tree is a nontrivial process in both the Weihrauch and reverse mathematics settings. Despite this, many combinatorial principles for trees are equivalent to their restrictions to trees with leaf…
A tree decomposition of the coordinates of a code is a mapping from the coordinate set to the set of vertices of a tree. A tree decomposition can be extended to a tree realization, i.e., a cycle-free realization of the code on the…
This work presents a method for semantic segmentation of mango trees in high resolution aerial imagery, and, a novel method for individual crown detection of mango trees using segmentation output. Mango Tree Net, a fully convolutional…
The weighted ancestor problem is a well-known generalization of the predecessor problem to trees. It is known to require $\Omega(\log\log n)$ time for queries provided $O(n\mathop{\mathrm{polylog}} n)$ space is available and weights are…
For a given directed tree and weights associated with vertices from a subtree the completion problem is to determine if these weights may be completed in a way to obtain a bounded weighted shift on the whole tree, which possibly satisfies…
This paper presents a new approach for trees-based regression, such as simple regression tree, random forest and gradient boosting, in settings involving correlated data. We show the problems that arise when implementing standard…
Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing…