Are there any good digraph width measures?

Many width measures for directed graphs have been proposed in the last few years in pursuit of generalizing (the notion of) treewidth to directed graphs. However, none of these measures possesses, at the same time, the major properties of treewidth, namely, 1. being algorithmically useful , that is, admitting polynomial-time algorithms for a large class of problems on digraphs of bounded width (e.g. the problems definable in MSO1MSO1); 2. having nice structural properties such as being (at least nearly) monotone under taking subdigraphs and some form of arc contractions (property closely related to characterizability by particular cops-and-robber games). We investigate the question whether the search for directed treewidth counterparts has been unsuccessful by accident, or whether it has been doomed to fail from the beginning. Our main result states that any reasonable width measure for directed graphs which satisfies the two properties above must necessarily be similar to treewidth of the underlying undirected graph

Width Parameterizations for Knot-Free Vertex Deletion on Digraphs

A knot in a directed graph G is a strongly connected subgraph Q of G with at least two vertices, such that no vertex in V(Q) is an in-neighbor of a vertex in V(G)V(Q). Knots are important graph structures, because they characterize the existence of deadlocks in a classical distributed computation model, the so-called OR-model. Deadlock detection is correlated with the recognition of knot-free graphs as well as deadlock resolution is closely related to the Knot-Free Vertex Deletion (KFVD) problem, which consists of determining whether an input graph G has a subset S subseteq V(G) of size at most k such that G[VS] contains no knot. Because of natural applications in deadlock resolution, KFVD is closely related to Directed Feedback Vertex Set. In this paper we focus on graph width measure parameterizations for KFVD. First, we show that: (i) KFVD parameterized by the size of the solution k is W[1]-hard even when p, the length of a longest directed path of the input graph, as well as kappa, its Kenny-width, are bounded by constants, and we remark that KFVD is para-NP-hard even considering many directed width measures as parameters, but in FPT when parameterized by clique-width; (ii) KFVD can be solved in time 2^{O(tw)} x n, but assuming ETH it cannot be solved in 2^{o(tw)} x n^{O(1)}, where tw is the treewidth of the underlying undirected graph. Finally, since the size of a minimum directed feedback vertex set (dfv) is an upper bound for the size of a minimum knot-free vertex deletion set, we investigate parameterization by dfv and we show that (iii) KFVD can be solved in FPT-time parameterized by either dfv+kappa or dfv+p. Results of (iii) cannot be improved when replacing dfv by k due to (i)

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

Towards a neocortically-inspired ab initio cellular model of associative memory

We are interested in self-organization and adaptation in intelligent systems that are robustly coupled with the real world. Such systems have a variety of sensory inputs that provide access to the richness, complexity, and noise of real-world signals. Specifically, the systems we design and implement are ab initio (simulated) spiking neural networks (SNNs) with cellular resolution and complex network topologies that evolve according to spike-timing dependent plasticity (STDP). We desire to understand how external signals (like speech, vision, etc.) are encoded in the dynamics of such SNNs. In particular, we desire to identify and confirm the extent to which various network-level measurements are information-preserving and could be used as the basis of an associative memory. The dissertation details the relevant background and results of a series of experiments designed to accomplish this objective. The results provide encouraging empirical evidence that such a model can be used for encoding attractors with multi-sensory inputs and across sensory modalities, which both emphasize the potential of such a model for use as a multi-modal associative memory

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Causal Inference from Statistical Data

The so-called kernel-based tests of independence are developed for automatic causal discovery between random variables from purely observational statistical data, i.e., without intervention. Beyond the independence relations, the complexity of conditional distriubtions is used as an additional inference principle of determining the causal ordering between variables. Experiments with simulated and real-world data show that the proposed methods surpass the state-of-the-art approaches