相关论文: A polynomial-time solution to the reducibility pro…

Various applications of graphs, in particular applications related to finding shortest paths, naturally get inputs with real weights on the edges. However, for algorithmic or visualization reasons, inputs with integer weights would often be…

In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique…

Interpreting three-leaf binary trees or {\em rooted triples} as constraints yields an entailment relation, whereby binary trees satisfying some rooted triples must also thus satisfy others, and thence a closure operator, which is known to…

We present a branch-and-bound algorithm to improve the lower bounds obtained by SONC/SAGE. The running time is fixed-parameter tractable in the number of variables. Furthermore, we describe a new heuristic to obtain a candidate for the…

We introduce the canonical reduction system of an element in an Artin-Tits group of spherical type, which generalizes the similar notion for braids (and mapping classes) introduced by Birman, Lubotzky and McCarthy. We show its basic…

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…

Our main contribution is a polynomial-time algorithm to reduce a $k$-colorable gammoid to a $(2k-2)$-colorable partition matroid. It is known that there are gammoids that can not be reduced to any $(2k-3)$-colorable partition matroid, so…

Reduction trees are a way of encoding a substitution procedure dictated by the relations of an algebra. We use reduction trees in the subdivision algebra to construct canonical triangulations of flow polytopes which are shellable. We…

In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…

Li-York theorem tells us that a period 3 orbit for a continuous map of the interval into itself implies the existence of a periodic orbit of every period. This paper concerns an analogue of the theorem for homeomorphisms of the…

We give an algebraic, determinant-based algorithm for the K-Cycle problem, i.e., the problem of finding a cycle through a set of specified elements. Our approach gives a simple FPT algorithm for the problem, matching the $O^*(2^{|K|})$…

Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups.…

In an earlier article [3], we presented an algorithm that can be used to rigorously check whether a specific cosine or sine polynomial is nonnegative in a given interval or not. The algorithm proves to be an indispensable tool in…

In this paper we give a detailed analysis of deterministic and randomized algorithms that enumerate any number of irreducible polynomials of degree $n$ over a finite field and their roots in the extension field in quasilinear where $N=n^2$…

An algorithm is proposed that solves two decision problems for pseudo-Anosov elements in the mapping class group of a surface with at least one marked fixed point. The first problem is the root problem: decide if the element is a power and…

We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm…

The automaton constrained tree knapsack problem is a variant of the knapsack problem in which the items are associated with the vertices of the tree, and we can select a subset of items that is accepted by a top-down tree automaton. If the…

P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not…

Given a Counting Monadic Second Order (CMSO) sentence $\psi$, the CMSO$[\psi]$ problem is defined as follows. The input to CMSO$[\psi]$ is a graph $G$, and the objective is to determine whether $G\models \psi$. Our main theorem states that…