Related papers: Some results on Vertex Separator Reconfiguration
We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent…
Graph separation is a central tool in parameterized algorithm design, and important separators are among its most successful ingredients. They yield small, structured families of separators that can be enumerated efficiently, and underlie…
Following the recent preprints arXiv:1903.09650 and arXiv:1906.04654 we comment on the feasibility of implementation of autodifferentiation in standard tensor network toolkits by briefly walking through the steps to do so. The total…
In a reconfiguration problem, we are given two feasible solutions of a combinatorial problem and our goal is to determine whether it is possible to reconfigure one into the other, with the steps dictated by specific reconfiguration rules.…
This paper is motivated by the vision of more efficient packet classification mechanisms that self-optimize in a demand-aware manner. At the heart of our approach lies a self-adjusting linear list data structure, where unlike in the classic…
In scheduling and timetabling applications, the mutual-exclusion constraint stipulates that certain pairs of tasks that cannot be executed at the same time. This corresponds to the vertex colouring problem in graph theory, for which there…
A primary challenge in metagenomics is reconstructing individual microbial genomes from the mixture of short fragments created by sequencing. Recent work leverages the sparsity of the assembly graph to find $r$-dominating sets which enable…
Dominators provide a general mechanism for identifying reconverging paths in graphs. This is useful for a number of applications in Computer-Aided Design (CAD) including signal probability computation in biased random simulation, switching…
In this paper we study a combinatorial reconfiguration problem that involves finding an optimal sequence of swaps to move an initial configuration of tokens that are placed on the vertices of a graph to a final desired one. This problem…
A $k$-coloring of a tournament is a partition of its vertices into $k$ acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a…
The hyperbolicity of a graph, informally, measures how close a graph is (metrically) to a tree. Hence, it is intuitively similar to treewidth, but the measures are formally incomparable. Motivated by the broad study of algorithms and…
This paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph and no two jobs connected by an edge are allowed to be assigned to the same machine. In particular, we study the case where the…
The $k$-vertex disjoint paths problem is one of the most studied problems in algorithmic graph theory. In 1994, Schrijver proved that the problem can be solved in polynomial time for every fixed $k$ when restricted to the class of planar…
In this paper, we review existing points-to Separation Logics for dynamic memory reasoning and we find that different usages of heap separation tend to be an obstacle. Hence, two total and strict spatial heap operations are proposed upon…
A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture postulates that every graph of order at least 3 is reconstructible. We show that interval graphs…
Parity games are games that are played on directed graphs whose vertices are labeled by natural numbers, called priorities. The players push a token along the edges of the digraph. The winner is determined by the parity of the greatest…
A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum…
We continue research into a well-studied family of problems that ask whether the vertices of a graph can be partitioned into sets $A$ and~$B$, where $A$ is an independent set and $B$ induces a graph from some specified graph class ${\cal…
We study the following independent set reconfiguration problem, called TAR-Reachability: given two independent sets $I$ and $J$ of a graph $G$, both of size at least $k$, is it possible to transform $I$ into $J$ by adding and removing…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…