In a multi-agent system where agents provide quantifiable work for each other on a voluntary basi... more In a multi-agent system where agents provide quantifiable work for each other on a voluntary basis, reputation mechanisms are incorporated to induce cooperation. Hereby agents assign their peers numerical scores based on their reported transaction histories. In such systems, adversaries can launch an attack by creating fake identities called Sybils, who report counterfeit transactions among one another, with the aim of increasing their own scores in the eyes of others. This paper provides new results about the Sybil-proofness of reputation mechanisms. We revisit the impossibility result of Seuken and Parkes (2011), who show that strongly-beneficial Sybil attacks cannot be prevented on reputation mechanisms satisfying three particular requirements. We prove that, under a more rigorous set of definitions of Sybil attack benefit, this result no longer holds. We characterise properties under which reputation mechanisms are susceptible to strongly-beneficial Sybil attacks. Building on ou...
Disclaimer/Complaints regulations If you believe that digital publication of certain material inf... more Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.
The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stat... more The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.
Hamiltonian paths By a Hamiltonian path in a graph G, we mean a path that visits every node exact... more Hamiltonian paths By a Hamiltonian path in a graph G, we mean a path that visits every node exactly once. Here, we will be interested in Hamiltonian paths between to given nodes s and t (we ignore the direction in which the path is traversed and only consider the set of edges on the path). Not every graph has a Hamiltonian path, and it is NP-hard to decide if a given graph has a Hamiltonian path between two given nodes. However, if we have one such path, we can sometimes conclude that there must be another.
An integer packing set is a set of non-negative integer vectors with the property that, if a vect... more An integer packing set is a set of non-negative integer vectors with the property that, if a vector $x$ is in the set, then every non-negative integer vector $y$ with $y \leq x$ is in the set as well. Integer packing sets appear naturally in Integer Optimization. In fact, the set of integer points in any packing polyhedron is an integer packing set. The main result of this paper is that integer packing sets, ordered by inclusion, form a well-quasi-ordering. This result allows us to answer a question recently posed by Bodur et al. In fact, we prove that the k-aggregation closure of any packing polyhedron is again a packing polyhedron. The generality of our main result allows us to provide a generalization to non-polyhedral sets: The k-aggregation closure of any downset of $\mathbb{R}^n_+$ is a packing polyhedron.
We show that any subset of $\mathbb{Z}_p^n$ ($p$ an odd prime) without $3$-term arithmetic progre... more We show that any subset of $\mathbb{Z}_p^n$ ($p$ an odd prime) without $3$-term arithmetic progression has size $O(p^{cn})$, where $c:=1-\frac{1}{18\log p}<1$. In particular, we find an upper bound of $O(2.84^n)$ on the maximum size of an affine cap in $GF(3)^n$.
In this paper, we give a constructive proof of the fact that the treewidth of a graph is at most ... more In this paper, we give a constructive proof of the fact that the treewidth of a graph is at most its divisorial gonality. The proof gives a polynomial time algorithm to construct a tree decomposition of width at most k, when an effective divisor of degree k that reaches all vertices is given. We also give a similar result for two related notions: stable divisorial gonality and stable gonality.
ABSTRACT This popularizing paper gives an exposition to a wide audience of bipartite matching the... more ABSTRACT This popularizing paper gives an exposition to a wide audience of bipartite matching theory. Through the example of marrying a set of men to a set of women, K\&quot;onigs theorem, Hall&#39;s marriage theorem and an algorithm for maximum size matching, are explained at an elementary level.
In a multi-agent system where agents provide quantifiable work for each other on a voluntary basi... more In a multi-agent system where agents provide quantifiable work for each other on a voluntary basis, reputation mechanisms are incorporated to induce cooperation. Hereby agents assign their peers numerical scores based on their reported transaction histories. In such systems, adversaries can launch an attack by creating fake identities called Sybils, who report counterfeit transactions among one another, with the aim of increasing their own scores in the eyes of others. This paper provides new results about the Sybil-proofness of reputation mechanisms. We revisit the impossibility result of Seuken and Parkes (2011), who show that strongly-beneficial Sybil attacks cannot be prevented on reputation mechanisms satisfying three particular requirements. We prove that, under a more rigorous set of definitions of Sybil attack benefit, this result no longer holds. We characterise properties under which reputation mechanisms are susceptible to strongly-beneficial Sybil attacks. Building on ou...
Disclaimer/Complaints regulations If you believe that digital publication of certain material inf... more Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.
The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stat... more The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.
Hamiltonian paths By a Hamiltonian path in a graph G, we mean a path that visits every node exact... more Hamiltonian paths By a Hamiltonian path in a graph G, we mean a path that visits every node exactly once. Here, we will be interested in Hamiltonian paths between to given nodes s and t (we ignore the direction in which the path is traversed and only consider the set of edges on the path). Not every graph has a Hamiltonian path, and it is NP-hard to decide if a given graph has a Hamiltonian path between two given nodes. However, if we have one such path, we can sometimes conclude that there must be another.
An integer packing set is a set of non-negative integer vectors with the property that, if a vect... more An integer packing set is a set of non-negative integer vectors with the property that, if a vector $x$ is in the set, then every non-negative integer vector $y$ with $y \leq x$ is in the set as well. Integer packing sets appear naturally in Integer Optimization. In fact, the set of integer points in any packing polyhedron is an integer packing set. The main result of this paper is that integer packing sets, ordered by inclusion, form a well-quasi-ordering. This result allows us to answer a question recently posed by Bodur et al. In fact, we prove that the k-aggregation closure of any packing polyhedron is again a packing polyhedron. The generality of our main result allows us to provide a generalization to non-polyhedral sets: The k-aggregation closure of any downset of $\mathbb{R}^n_+$ is a packing polyhedron.
We show that any subset of $\mathbb{Z}_p^n$ ($p$ an odd prime) without $3$-term arithmetic progre... more We show that any subset of $\mathbb{Z}_p^n$ ($p$ an odd prime) without $3$-term arithmetic progression has size $O(p^{cn})$, where $c:=1-\frac{1}{18\log p}<1$. In particular, we find an upper bound of $O(2.84^n)$ on the maximum size of an affine cap in $GF(3)^n$.
In this paper, we give a constructive proof of the fact that the treewidth of a graph is at most ... more In this paper, we give a constructive proof of the fact that the treewidth of a graph is at most its divisorial gonality. The proof gives a polynomial time algorithm to construct a tree decomposition of width at most k, when an effective divisor of degree k that reaches all vertices is given. We also give a similar result for two related notions: stable divisorial gonality and stable gonality.
ABSTRACT This popularizing paper gives an exposition to a wide audience of bipartite matching the... more ABSTRACT This popularizing paper gives an exposition to a wide audience of bipartite matching theory. Through the example of marrying a set of men to a set of women, K\&quot;onigs theorem, Hall&#39;s marriage theorem and an algorithm for maximum size matching, are explained at an elementary level.
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