Formation control is concerned with the design of control laws that stabilize agents at given distances from each other, with the constraint that an agent’s dynamics can depend only on a subset of other agents. When the information flow graph of the system, which encodes this dependency, is acyclic, simple control laws are known to globally stabilize the system, save for a set of measure zero o...

In this paper, network error control coding is studied for robust and efficient multicast in a directed acyclic network with imperfect links. The block network error control coding framework, BNEC, is presented and the capability of the scheme to correct a mixture of symbol errors and packet erasures and to detect symbol errors is studied. The idea of syndrome-based decoding and error detection...

II Preface This is a Master's thesis written at the department of Mathematics at the Royal Institute of Technology (KTH) in Stockholm, supervised by Svante Linusson. It is assumed that the reader has studied mathematics at an undergraduate level, and that he is well acquainted with some basic graph theory concepts such as paths and cycles. III Summary This paper is about acyclic orientations of...

We consider the maximization version of the edge-disjoint path problem (EDP). In undirected graphs and directed acyclic graphs, we obtain an O( √ n) upper bound on the approximation ratio where n is the number of nodes in the graph. We show this by establishing the upper bound on the integrality gap of the natural relaxation based on multicommodity flows. Our upper bound matches within a consta...

Datasets from several domains, such as life-sciences, semantic web, machine learning, natural language processing, etc. are naturally structured as acyclic graphs. These datasets, particularly those in bio-informatics and computational epidemiology, have grown tremendously over the last decade or so. Increasingly, as a consequence, there is a need to build and evaluate various strategies for pr...

We consider the maximization version of the edge-disjoint path problem (EDP). In undirected graphs and directed acyclic graphs, we obtain an O( √ n) upper bound on the approximation ratio where n is the number of nodes in the graph. We show this by establishing the upper bound on the integrality gap of the natural relaxation based on multicommodity flows. Our upper bound matches within a consta...

We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite acyclic directed graph admits countably many structures of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras assoc...

Strategy improvement is a widely-used and well-studied class of algorithms for solving graph-based infinite games. These algorithms are parametrized by a switching rule, and one of the most natural rules is “all switches” which switches as many edges as possible in each iteration. Continuing a recent line of work, we study all-switches strategy improvement from the perspective of computational ...

We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite directed acyclic graph admits a structure of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras associated to those...