Related papers: Space Saving by Dynamic Algebraization
There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…
Given two integers $\ell$ and $p$ as well as $\ell$ graph classes $\mathcal{H}_1,\ldots,\mathcal{H}_\ell$, the problems $\mathsf{GraphPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell,p)$, \break $\mathsf{VertPart}(\mathcal{H}_1, \ldots,…
In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $\Delta n$ edges such that $\Delta \geq…
$H$-Packing is the problem of finding a maximum number of vertex-disjoint copies of $H$ in a given graph $G$. $H$-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of $G$ exactly once. Our goal…
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the…
In this paper, we have developed a fully-dynamic algorithm for maintaining cardinality of maximum-matching in a tree using the construction of top-trees. The time complexities are as follows: 1. Initialization Time: $O(n(log(n)))$ to build…
We show that there is a polynomial space algorithm that counts the number of perfect matchings in an $n$-vertex graph in $O^*(2^{n/2})\subset O(1.415^n)$ time. ($O^*(f(n))$ suppresses functions polylogarithmic in $f(n)$).The previously…
We propose a general method for combinatorial online learning problems whose offline optimization problem can be solved efficiently via a dynamic programming algorithm defined by an arbitrary min-sum recurrence. Examples include online…
We revisit a graph width parameter that we dub bipartite treewidth (btw). Bipartite treewidth can be seen as a common generalization of treewidth and the odd cycle transversal number, and is closely related to odd-minors. Intuitively, a…
For many algorithmic problems on graphs of treewidth $t$, a standard dynamic programming approach gives an algorithm with time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. It turns out that when one considers the more…
In this paper we study a natural generalization of both {\sc $k$-Path} and {\sc $k$-Tree} problems, namely, the {\sc Subgraph Isomorphism} problem. In the {\sc Subgraph Isomorphism} problem we are given two graphs $F$ and $G$ on $k$ and $n$…
Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in K-dimensional space such that the…
While the algorithmic drawing of static trees is well-understood and well-supported by software tools, creating animations depicting how a tree changes over time is currently difficult: software support, if available at all, is not…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…
Tree-decompositions and treewidth are of fundamental importance in structural and algorithmic graph theory. The "spread" of a tree-decomposition is the minimum integer $s$ such that every vertex lies in at most $s$ bags. A…
Dynamic programming is a mathematical optimization method and a computer programming method as well. In this paper, the notion of sheaf programming in topological spaces is introduced and it is demonstrated that it relates very well to the…
We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…