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Robert Brijder

Publications and source records attributed to Robert Brijder.

At least 19 recordsLinked to original sources
arXiv2026

GraphAlg Playground: An Online Platform for Learning and Experimenting with the GraphAlg Language

The GraphAlg language for graph algorithms enables native support for user-defined graph analytics workloads in databases. In this demonstration, we present a web-based playground for writing and executing GraphAlg programs in the web browser, including an interactive tutorial explaining its key concepts. The playground runs inside the user's web browser without any installation, and is freely available under a permissive license as a reusable library. We present two demonstration scenarios of the publicly available playground website, showing how new users can learn to program in GraphAlg using the tutorial, while expert users can use the playground to prototype and validate their algorithms.

cs.DB↗
arXiv2026

Foundations of the GraphAlg Language

The GraphAlg domain-specific language for graph algorithms enables user-defined algorithms in graph databases. In this work we show how GraphAlg is built on top of the formal MATLANG language for matrix manipulation. Starting from MATLANG, we describe the extensions to MATLANG and the syntactic sugar needed to derive GraphAlg. Furthermore, we prove that any GraphAlg program can be simulated in an extension of for-MATLANG that supports simultaneous induction.

cs.DB↗
arXiv2026

Algorithm Support for Graph Databases, Done Right

Graph database query languages cannot express algorithms like PageRank, forcing costly data wrangling, while existing solutions such as algorithm libraries, vertex-centric APIs, and recursive CTEs lack the necessary combination of expressiveness, performance, and usability. We present GraphAlg: a domain-specific language for graph algorithms that compiles to relational algebra, enabling seamless integration with query processing pipelines. Built on linear algebra foundations, GraphAlg provides intuitive matrix operations that are amenable to aggressive optimization including sparsity analysis, loop-invariant code motion, and in-place aggregation. Our implementation in AvantGraph demonstrates significant code complexity reduction compared to SQL/Python and Pregel while achieving excellent performance on LDBC Graphalytics benchmarks. GraphAlg establishes that graph databases can serve as unified platforms for both queries and analytics.

cs.DB↗
arXiv2021

A Characterization of Circle Graphs in Terms of Total Unimodularity

A graph $G$ has an associated multimatroid $\mathcal{Z}_3(G)$, which is equivalent to the isotropic system of $G$ studied by Bouchet. In previous work it was shown that $G$ is a circle graph if and only if for every field $\mathbb F$, the rank function of $\mathcal{Z}_3(G)$ can be extended to the rank function of an $\mathbb F$-representable matroid. In the present paper we strengthen this result using a multimatroid analogue of total unimodularity. As a consequence we obtain a characterization of matroid planarity in terms of this total-unimodularity analogue.

math.CO↗
arXiv2019

A Characterization of Circle Graphs in Terms of Multimatroid Representations

The isotropic matroid $M[IAS(G)]$ of a looped simple graph $G$ is a binary matroid equivalent to the isotropic system of $G$. In general, $M[IAS(G)]$ is not regular, so it cannot be represented over fields of characteristic $\neq 2$. The ground set of $M[IAS(G)]$ is denoted $W(G)$; it is partitioned into 3-element subsets corresponding to the vertices of $G$. When the rank function of $M[IAS(G)]$ is restricted to subtransversals of this partition, the resulting structure is a multimatroid denoted $\mathcal{Z}_{3}(G)$. In this paper we prove that $G$ is a circle graph if and only if for every field $\mathbb{F}$, there is an $\mathbb{F}$-representable matroid with ground set $W(G)$, which defines $\mathcal{Z}_{3}(G)$ by restriction. We connect this characterization with several other circle graph characterizations that have appeared in the literature.

math.CO↗
arXiv2019

On matrices and $K$-relations

We show that the matrix query language $\mathsf{MATLANG}$ corresponds to a natural fragment of the positive relational algebra on $K$-relations. The fragment is defined by introducing a composition operator and restricting $K$-relation arities to two. We then proceed to show that $\mathsf{MATLANG}$ can express all matrix queries expressible in the positive relational algebra on $K$-relations, when intermediate arities are restricted to three. Thus we offer an analogue, in a model with numerical data, to the situation in classical logic, where the algebra of binary relations is equivalent to first-order logic with three variables.

cs.DB↗
arXiv2018

Computing with Chemical Reaction Networks: A Tutorial

Chemical reaction networks (CRNs) model the behavior of chemical reactions in well-mixed solutions and they can be designed to perform computations. In this tutorial we give an overview of various computational models for CRNs. Moreover, we discuss a method to implement arbitrary (abstract) CRNs in a test tube using DNA. Finally, we discuss relationships between CRNs and other models of computation.

cs.ET↗
arXiv2017

On the expressive power of query languages for matrices

We investigate the expressive power of $\mathsf{MATLANG}$, a formal language for matrix manipulation based on common matrix operations and linear algebra. The language can be extended with the operation $\mathsf{inv}$ of inverting a matrix. In $\mathsf{MATLANG}+\mathsf{inv}$ we can compute the transitive closure of directed graphs, whereas we show that this is not possible without inversion. Indeed we show that the basic language can be simulated in the relational algebra with arithmetic operations, grouping, and summation. We also consider an operation $\mathsf{eigen}$ for diagonalizing a matrix, which is defined so that different eigenvectors returned for a same eigenvalue are orthogonal. We show that $\mathsf{inv}$ can be expressed in $\mathsf{MATLANG}+\mathsf{eigen}$. We put forward the open question whether there are boolean queries about matrices, or generic queries about graphs, expressible in $\mathsf{MATLANG} + \mathsf{eigen}$ but not in $\mathsf{MATLANG}+\mathsf{inv}$. The evaluation problem for $\mathsf{MATLANG} + \mathsf{eigen}$ is shown to be complete for the complexity class $\exists \mathbf{R}$.

cs.DB↗
arXiv2017

Orienting Transversals and Transition Polynomials of Multimatroids

Multimatroids generalize matroids, delta-matroids, and isotropic systems, and transition polynomials of multimatroids subsume various polynomials for these latter combinatorial structures, such as the interlace polynomial and the Tutte-Martin polynomial. We prove evaluations of the Tutte-Martin polynomial of isotropic systems from Bouchet directly and more efficiently in the context of transition polynomials of multimatroids. Moreover, we generalize some related evaluations of the transition polynomial of 4-regular graphs from Jaeger to multimatroids. These evaluations are obtained in a uniform and matroid-theoretic way. We also translate the evaluations in terms of the interlace polynomial of graphs. Finally, we give an excluded-minor theorem for the class of binary tight 3-matroids (a subclass of multimatroids) based on the excluded-minor theorem for the class of binary delta-matroids from Bouchet.

math.CO↗
arXiv2017

Democratic, Existential, and Consensus-Based Output Conventions in Stable Computation by Chemical Reaction Networks

We show that some natural output conventions for error-free computation in chemical reaction networks (CRN) lead to a common level of computational expressivity. Our main results are that the standard consensus-based output convention have equivalent computational power to (1) existence-based and (2) democracy-based output conventions. The CRNs using the former output convention have only "yes" voters, with the interpretation that the CRN's output is yes if any voters are present and no otherwise. The CRNs using the latter output convention define output by majority vote among "yes" and "no" voters. Both results are proven via a generalized framework that simultaneously captures several definitions, directly inspired by a Petri net result of Esparza, Ganty, Leroux, and Majumder [CONCUR 2015]. These results support the thesis that the computational expressivity of error-free CRNs is intrinsic, not sensitive to arbitrary definitional choices.

cs.ET↗
arXiv2017

Isotropic matroids III: Connectivity

The isotropic matroid $M[IAS(G)]$ of a graph $G$ is a binary matroid, which is equivalent to the isotropic system introduced by Bouchet. In this paper we discuss four notions of connectivity related to isotropic matroids and isotropic systems. We show that the isotropic system connectivity defined by Bouchet is equivalent to vertical connectivity of $M[IAS(G)]$, and if $G$ has at least four vertices, then $M[IAS(G)]$ is vertically 5-connected if and only if $G$ is prime (in the sense of Cunningham's split decomposition). We also show that $M[IAS(G)]$ is $3$-connected if and only if $G$ is connected and has neither a pendant vertex nor a pair of twin vertices. Our most interesting theorem is that if $G$ has $n\geq7$ vertices then $M[IAS(G)]$ is not vertically $n$-connected. This abstract-seeming result is equivalent to the more concrete assertion that $G$ is locally equivalent to a graph with a vertex of degree $<\frac{n-1}{2}$.

math.CO↗
arXiv2017

Sorting by Reversals and the Theory of 4-Regular Graphs

We show that the theory of sorting by reversals fits into the well-established theory of circuit partitions of 4-regular multigraphs (which also involves the combinatorial structures of circle graphs and delta-matroids). In this way, we expose strong connections between the two theories that have not been fully appreciated before. We also discuss a generalization of sorting by reversals involving the double-cut-and-join (DCJ) operation. Finally, we also show that the theory of sorting by reversals is closely related to that of gene assembly in ciliates.

cs.DM↗
arXiv2017

Conditions for Extinction Events in Chemical Reaction Networks with Discrete State Spaces

We study chemical reaction networks with discrete state spaces, such as the standard continuous time Markov chain model, and present sufficient conditions on the structure of the network that guarantee the system exhibits an extinction event. The conditions we derive involve creating a modified chemical reaction network called a domination-expanded reaction network and then checking properties of this network. We apply the results to several networks including an EnvZ-OmpR signaling pathway in Escherichia coli. This analysis produces a system of equalities and inequalities which, in contrast to previous results on extinction events, allows algorithmic implementation. Such an implementation will be investigated in a companion paper where the results are applied to 458 models from the European Bioinformatics Institute's BioModels database.

math.DS↗
arXiv2016

Isotropic matroids I: Multimatroids and neighborhoods

Several properties of the isotropic matroid of a looped simple graph are presented. Results include a characterization of the multimatroids that are associated with isotropic matroids and several ways in which the isotropic matroid of G incorporates information about graphs locally equivalent to G. Specific results of the latter type include a characterization of graphs that are locally equivalent to bipartite graphs, a direct proof that two forests are isomorphic if and only if their isotropic matroids are isomorphic, and a way to express local equivalence indirectly, using only edge pivots.

math.CO↗
arXiv2015

Minimal Output Unstable Configurations in Chemical Reaction Networks and Deciders

We study the set of output stable configurations of chemical reaction deciders (CRDs). It turns out that CRDs with only bimolecular reactions (which are almost equivalent to population protocols) have a special structure that allows for an algorithm to efficiently compute their finite set of minimal output unstable configurations. As a consequence, a relatively large set of configurations may be efficiently checked for output stability. We also provide a number of observations regarding the semilinearity result of Angluin et al. [Distrib. Comput., 2007] from the context of population protocols (which is a central result for output stable CRDs). In particular, we observe that the computation-friendly class of totally stable CRDs has equal expressive power as the larger class of output stable CRDs.

cs.CC↗