ACiD Seminars 2016/17 
Term 1 
Thu 20 Oct 2016 12:00 in E245 
Vadim Lozin (Warwick)
Breaking the boundaries: from structure to algorithms
Show Abstract
Finding a maximum independent set in a graph is an NPhard problem.
However, restricted to the class of line graphs this problem becomes
polynomialtime solvable due to the celebrated matching algorithm of
Jack Edmonds. What makes the problem easy in the class of line graphs
and what other restrictions can lead to an efficient solution? To answer
these questions, we employ the notion of boundary classes of graphs.
In this talk, we shed some light on the structure of the boundary separating
difficult instances of the problem from polynomially solvable ones and
analyze tools to break it. We also discuss similar questions with respect
to some other algorithmic problems.

Mon 24 Oct 2016 16:00 in E245 
Barny Martin (Durham)
The Complexity of Quantified Constraints
Show Abstract
We elaborate the complexity of the Quantified Constraint Satisfaction Problem, QCSP(A), where A is a finite idempotent algebra. Such a problem is either in NP or is coNPhard, and the borderline is given precisely according to whether A enjoys the polynomiallygenerated powers (PGP) property. This reduces the complexity classification problem for QCSPs to that of CSPs, modulo that coNPhard cases might have complexity rising up to Pspacecomplete. Our result requires infinite languages, but in this realm represents the proof of a slightly weaker form of a conjecture for QCSP complexity made by Hubie Chen in 2012. The result relies heavily on the algebraic dichotomy between PGP and exponentiallygenerated powers (EGP), proved by Dmitriy Zhuk in 2015, married carefully to previous work of Chen.

Mon 31 Oct 2016 16:00 in E245 
Andre Nichterlein (Durham)
On parameterized algorithms for polynomialtime solvable problems
Show Abstract
Parameterized complexity analysis is a flourishing field dealing with the exact solvability of "intractable" problems. Appropriately parameterizing polynomialtime solvable problems helps reducing unattractive polynomial running times. In particular, this "FPT in P" approach sheds new light on what makes a problem far from being solvable in linear time, in the same way as classical FPT algorithms help in illuminating what makes an NPhard problem far from being solvable in polynomial time. Surprisingly, this very interesting research direction has been too little explored so far; the known results are rather scattered and do not systematically refer to or exploit the toolbox of parameterized algorithm design.
In this talk I outline known results, explain some of the corresponding techniques, and highlight similarities and differences to the classical design of parameterized algorithms for NPhard problems.

Mon 7 Nov 2016 16:00 in E245 
Argyris Deligkas (Liverpool)
The complexity of Greedy Matching
Show Abstract
Motivated by the fact that in several cases a matching in a graph is stable if and only if it is produced by a greedy algorithm, we study the problem of computing a maximum weight greedy matching on weighted graphs, termed GreedyMatching.
In wide contrast to the maimum weight matching problem, for which many efficient algorithms are known, we prove that GreedyMatching is strongly NPhard and APXcomplete, and thus it does not admit a PTAS unless P=NP, even on graphs with maximum degree at most 3 and with at most three different integer edge weights. Furthermore we prove that GreedyMatching is strongly NPhard if the input graph is in addition bipartite. Moreover we consider two natural parameters of the problem, for which we establish a sharp threshold behavior between NPhardness and tractability.
On the positive side, we present a randomized approximation algorithm (Rgma) for GreedyMatching on a special class of weighted graphs, called bush graphs. We highlight an unexpected connection between Rgma and the approximation of maximum cardinality matching in unweighted graphs via randomized greedy algorithms. We show that, if the approximation ratio of Rgma is ρ, then for every ε > 0 the randomized Mrg algorithm gives a (ρ − ε)approximation for the maximum cardinality matching. We conjecture that a tight bound for ρ is 2 ; we prove our conjecture true for two subclasses of bush graphs. Proving a tight bound for the approximation ratio of Mrg on unweighted graphs (and thus also proving a tight value for ρ) is a longstanding open problem. This unexpected relation of our Rgma algorithm with the Mrg algorithm may provide new insights
for solving this problem.
This is joint work with George Mertzios and Paul Spirakis

Mon 14 Nov 2016 16:00 in E245 
Wolfram Bentz (Hull)
Synchronisation for Automata, Semigroups, and Groups
Show Abstract
Synchronisation is a property of automata and can be understood as a method of error recovery. An automaton is synchronising if there is an input sequence which always brings the automaton into a known state irrespectively of the original state of the automaton. Such a sequence is called a reset (or synchronising) word.
We can translate this question into the realm of semigroup theory by asking if the transition semigroup associated to the automaton contains a constant map. Similarly, we say a permutation group is synchronising if it generates a synchronising semigroup together with any noninvertible transformation.
Primitivity of a group is a strong property that is required for synchronisation and ``usually´´ also forces synchronisation. Our work examines how usual this situation actually is.
Our results use an auxiliary graph construction that enables us to approach the problem by combinatorial methods.
This is a joint work with Joao Araujo (CEMAT, University of Lisbon), Peter J. Cameron (Mathematical Institute, University of St Andrews), Gordon Royle (Centre for the Mathematics of Symmetry and Computation, University of Western Australia), and Artur Schaefer (Mathematical Institute, University of St Andrews).

Mon 21 Nov 2016 16:00 in E245 
Nic Georgiou (Durham Maths)
Winkler's hat game on graphs
Show Abstract
Hat games are a popular topic in combinatorics with connections to coding theory, network coding and auctions. In a typical hat game, a team of $n$ players play against a single adversary. The adversary places a coloured hat (from a choice of $q$ different colours) on each player and each player tries to guess the colour of the hat they are wearing by looking at the colours of the hats worn by some of the other players.
Many variations on this basic theme exist; we consider the game where all players must guess simultaneously, and the team wins if they have a deterministic strategy where at least one person guesses correctly for each one of the $q^n$ possible configurations of hats. Each player only sees a subset of the hats, as determined by a graph: each vertex in the graph represents a player and each player sees only the hats of his/her neighbours in the graph. If there is a winning strategy for the graph $G$ when the game is played with $q$ different colours, we say that $G$ is $q$solvable.
I will present some constructions for general $q$ which yield two classes of $q$solvable graphs:
i) bipartite, but large, graphs (i.e., number of vertices exponential in $q$);
ii) graphs with largest clique of size $\epsilon q$, and number of vertices linear in $q$, for any $\epsilon > 0$;
and discuss some related open problems.
This is joint work with Maximilien Gadouleau.

Mon 28 Nov 2016 16:00 in E245 
Victor Dalmau (University Pompeu Fabra, Barcelona)
Approximation of MIN CSP
Show Abstract
An instance of the constraint satisfaction problem (CSP) is
given by a family of constraints on overlapping sets of variables, and
the goal is to assign values from a fixed domain to the variables so
that all constraints are satisfied. In the optimization version, the
goal is to maximize the number of satisfied constraints (MAX CSP) or,
alternatively, to minimize the number of unsatisfied constraints (MIN
CSP). This problem is usually parameterized by the set, Gamma, of
relations allowed in the constraints, usually called constraint
language. It turns out that MAX CSP/MIN CSP is computationally hard for
most constraint languages, which motivates the study of approximation
algorithms. In this talk we will focus on the approximation of MIN CSPs.
We shall start addressing the following question: which constraint
languages give rise to a MIN CSPs that is constantfactor approximable?
We shall also study some other weaker approximation notions such
polynomial loss and robust approximation.

Mon 5 Dec 2016 16:00 in E245 
(postponed)

Mon 12 Dec 2016 16:00 in E245 
Stefano Giani (Durham Engineering)
Why mesh adaptivity?
Show Abstract
Mesh adaptivity is becoming a very useful tool to improve the accuracy of finite element simulations.
The general idea behind mesh adaptivity is to enrich the finite element space where it is necessary to reduce the error and introducing the smallest number of extra degrees of freedom. In many cases the most advanced adaptive techniques can achieve exponential convergence to the right solution.
In the first part of this talk we would like to give an overview of current mesh adaptivity techniques.
In the second part we present a different kind of adaptivity based on aggregation that can be used to solve efficiently problems on complicated domains.
In the third and final part we explore how finite element aggregation can be used to construct preconditioners.

Term 2 
Mon 16 Jan 2017 16:00 in E245 
Cedric Gerot (Grenoble)
When can Boxspline subdivision be factorised into elementary steps?
Show Abstract
Boxsplines are local, possibly anisotropic, piecewise polynomial functions whose integer translates make up a partition of unity. They also satisfy a refinement equation yielding to a subdivision scheme which, if it can be factorised into elementary steps, can be implemented inplace, and be the prediction operator of a biorthogonal multiresolution framework with Boxsplines as scaling functions. However, every Boxspline cannot be factorised into elementary steps. We give a necessary and sufficient condition and a sketch of proof which involves linear and commutative algebra.

Mon 23 Jan 2017 16:00 in E245 
Isolde Adler (Leeds)

Wed 25 Jan 2017 13:00 in E245 
Kitty Meeks (Glasgow)

Mon 30 Jan 2017 16:00 in E245 
Viktor Zamaraev (Warwick)
On forbidden induced subgraphs for unit disk graphs
Show Abstract
A unit disk graph is the intersection graph of disks of equal radii in
the plane. The class of unit disk graphs is hereditary, and therefore
can be characterized in terms of minimal forbidden induced subgraphs.
In spite of quite active study of unit disk graphs very little is
known about minimal forbidden induced subgraphs for this class. We
found only finitely many minimal non unit disk graphs in the
literature. In this paper, we study in a systematic way forbidden
induced subgraphs for the class of unit disk graphs. We develop
several structural and geometrical tools, and use them to reveal
infinitely many new minimal non unit disk graphs. Further, we use
these results to investigate the structure of cobipartite unit disk
graphs. In particular, we give a structural characterization of those
cobipartite unit disk graphs whose edges between parts form a
C_4free bipartite graph and show that bipartite complements of these
graphs are also unit disk graphs. Our results lead us to propose a
conjecture that the class of cobipartite unit disk graphs is closed
under bipartite complementation.
Based on joint work with Aistis Atminas.

Wed 8 Feb 2016 13:00 in E245 
Maciej Koutny (Newcastle)
Synthesis of Petri Nets with Wholeplace Operations and Localities
Show Abstract
Synthesising systems from behavioural specifications is an attractive way of constructing implementations which are correctbydesign and thus requiring no costly validation efforts. In this talk, systems are modelled by Petri nets and the behavioural specifications are
provided in the form of step transition systems, where arcs are labelled by multisets of executed actions. We focus on the problem of synthesising Petri nets with wholeplace operations and localities, which are a class of Petri nets powerful enough to express a wide range of system behaviours, including inhibition of actions, resetting of local states, and locally maximal executions.

Mon 13 Feb 2017 16:00 in E245 
Iddo Tzameret (Royal Holloway)

Mon 20 Feb 2017 16:00 in E245 
Stefan Dantchev (Durham)

Mon 27 Feb 2017 16:00 in E245 
Ojoung Kwon (TU Berlin, Germany)

Mon 6 Mar 2017 16:00 in E245 
Tom Friedetzky (Durham)
Tweaking randomised load balancing approaches, part 1
We will be discussing several load balancing mechanisms based on
ballsintobins protocols and random walks. Our focus will be on making
standard models more applicable, e.g., by allowing to model tasks sizes and
processing speeds, or by attempting to "parallelise" inherently
sequentialseeming protocols. This will be more of an overview talk light
on proofs (though main ideas and techniques will be discussed).
The many authors involved in the various pieces of work will be duly
mentioned during the talk.

Mon 13 Mar 2017 16:00 in E245 
Tom Friedetzky (Durham)
Tweaking randomised load balancing approaches, part 2
We will be discussing several load balancing mechanisms based on
ballsintobins protocols and random walks. Our focus will be on making
standard models more applicable, e.g., by allowing to model tasks sizes and
processing speeds, or by attempting to "parallelise" inherently
sequentialseeming protocols. This will be more of an overview talk light
on proofs (though main ideas and techniques will be discussed).
The many authors involved in the various pieces of work will be duly
mentioned during the talk.
