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Weakly Modular Graphs and Nonpositive Curvature
This article investigates structural, geometrical, and topological characteri-zations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various “nonpositive cur-vature” and “local-to-global” properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a far-reaching common generalization of median graphs (and more generally, of mod-ular and orientable modular graphs), Helly graphs, bridged graphs, and dual polar graphs occurring under different disguises (1–skeletons, collinearity graphs, covering graphs, domains, etc.) in several seemingly-u...
Algorithms and Discrete Applied Mathematics
This book collects the refereed proceedings of the Second International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2016, held in Thiruvananthapuram, India, in February 2016. The volume contains 30 full revised papers from 90 submissions along with 1 invited talk presented at the conference. The conference focuses on topics related to efficient algorithms and data structures, their analysis (both theoretical and experimental) and the mathematical problems arising thereof, and new applications of discrete mathematics, advances in existing applications and development of new tools for discrete mathematics.
STACS 2002
This book constitutes the refereed proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2002, held in Antibes - Juan les Pins, France, in March 2002. The 50 revised full papers presented together with three invited papers were carefully reviewed and selected from a total of 209 submissions. The book offers topical sections on algorithms, current challenges, computational and structural complexity, automata and formal languages, and logic in computer science.
Topological Data Analysis
This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.
Be sparse! Be dense! Be robust!
In this thesis we study the computational complexity of five NP-hard graph problems. It is widely accepted that, in general, NP-hard problems cannot be solved efficiently, that is, in polynomial time, due to many unsuccessful attempts to prove the contrary. Hence, we aim to identify properties of the inputs other than their length, that make the problem tractable or intractable. We measure these properties via parameters, mappings that assign to each input a nonnegative integer. For a given parameter k, we then attempt to design fixed-parameter algorithms, algorithms that on input q have running time upper bounded by f(k(q)) * |q|^c , where f is a preferably slowly growing function, |q| is t...
Intense Automorphisms of Finite Groups
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Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques
This book constitutes the joint refereed proceedings of the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and the 9th International Workshop on Randomization and Computation, RANDOM 2005, held in Berkeley, CA, USA in August 2005. The volume contains 41 carefully reviewed papers, selected by the two program committees from a total of 101 submissions. Among the issues addressed are design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and c...
Reachability Problems
This book constitutes the refereed proceedings of the 12th International Conference on Reachability Problems, RP 2018, held in Marseille, France, in September 2018. The 11 full papers presented were carefully reviewed and selected from 21 submissions. The papers cover topics such as reachability for infinite state systems; rewriting systems; reachability analysis in counter/timed/cellular/communicating automata; Petri nets; computational aspects of semigroups, groups, and rings; reachability in dynamical and hybrid systems; frontiers between decidable and undecidable reachability problems; complexity and decidability aspects; predictability in iterative maps, and new computational paradigms.
Algorithms for Sensor Systems
This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Workshop on Algorithms for Sensor Systems, Wireless Ad Hoc Networks, and Autonomous Mobile Entities, ALGOSENSORS 2010, held in Bordeaux, France, in July 2010. The 15 full papers and two brief announcements were carefully reviewed and selected from 31 submissions. The workshop aimed at bringing together research contributions related to diverse algorithmic and complexity-theoretic aspects of wireless sensor networks. In 2010 the focus was extended to comprise also contributions about related types of networks such as ad hoc wireless networks, mobile networks, radio networks and distributed systems of robots.
Existence of Unimodular Triangulations–Positive Results
Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.
