相关论文: The Knowlton-Graham partition problem

A partition on [n] has an m-nesting if there exists i_1 < i_2 < ... < i_m < j_m < j_{m-1} < ... < j_1, where i_l and j_l are in the same block for all 1 <= l <= m. We use generating trees to construct the class of partitions with no…

This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under which a sequence is necessarily connected i.e. the sequence…

The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…

The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this…

In this note we discuss the problem of finding the nth power of a matrix which is strongly connected to the study of Markov chains and others mathematical topics. We observe the known fact (but maybe not well known) that the Cayley-Hamilton…

This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be…

We develop a computation model for solving Boolean networks that implements wires through quantum ground-state computation and implements gates through identities following from angular momentum algebra and statistics. The gates are static…

The notion of degree-constrained spanning hierarchies, also called k-trails, was recently introduced in the context of network routing problems. They describe graphs that are homomorphic images of connected graphs of degree at most k. First…

Given a finite grid in $\mathbb{R}^2$, how many lines are needed to cover all but one point at least $k$ times? Problems of this nature have been studied for decades, with a general lower bound having been established by Ball and Serra. We…

We study the following combinatorial problem. Given a set of $n$ y-monotone curves, which we call wires, a tangle determines the order of the wires on a number of horizontal layers such that any two consecutive layers differ only in swaps…

In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…

In this paper we study formulations and algorithms for the cycle clustering problem, a partitioning problem over the vertex set of a directed graph with nonnegative arc weights that is used to identify cyclic behavior in simulation data…

We present a conceptually simple yet effective algorithm to detect wireframes in a given image. Compared to the previous methods which first predict an intermediate heat map and then extract straight lines with heuristic algorithms, our…

Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…

Partitioning large matrices is an important problem in distributed linear algebra computing (used in ML among others). Briefly, our goal is to perform a sequence of matrix algebra operations in a distributed manner (whenever possible) on…

Recently, a novel method based on coding partitions [1]-[4] has been used to derive power series expansions to previously intractable problems. In this method the coefficients at $k$ are determined by summing the contributions made by each…

Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…

This paper introduces two matrix analogues for set partitions. A composition matrix on a finite set X is an upper triangular matrix whose entries partition X, and for which there are no rows or columns containing only empty sets. A…

Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…

Finding the solutions to a system of multivariate polynomial equations is a fundamental problem in mathematics and computer science. It involves evaluating the polynomials at many points, often chosen from a grid. In most current methods,…