Network Interdiction Using Adversarial Traffic Flows

Traditional network interdiction refers to the problem of an interdictor trying to reduce the throughput of network users by removing network edges. In this paper, we propose a new paradigm for network interdiction that models scenarios, such as stealth DoS attack, where the interdiction is performed through injecting adversarial traffic flows. Under this paradigm, we first study the deterministic flow interdiction problem, where the interdictor has perfect knowledge of the operation of network users. We show that the problem is highly inapproximable on general networks and is NP-hard even when the network is acyclic. We then propose an algorithm that achieves a logarithmic approximation ratio and quasi-polynomial time complexity for acyclic networks through harnessing the submodularity of the problem. Next, we investigate the robust flow interdiction problem, which adopts the robust optimization framework to capture the case where definitive knowledge of the operation of network users is not available. We design an approximation framework that integrates the aforementioned algorithm, yielding a quasi-polynomial time procedure with poly-logarithmic approximation ratio for the more challenging robust flow interdiction. Finally, we evaluate the performance of the proposed algorithms through simulations, showing that they can be efficiently implemented and yield near-optimal solutions

Parametric LTL on Markov Chains

This paper is concerned with the verification of finite Markov chains against parametrized LTL (pLTL) formulas. In pLTL, the until-modality is equipped with a bound that contains variables; e.g., $\Diamond_{\le x}\ \varphi$ asserts that $\varphi$ holds within $x$ time steps, where $x$ is a variable on natural numbers. The central problem studied in this paper is to determine the set of parameter valuations $V_{\prec p} (\varphi)$ for which the probability to satisfy pLTL-formula $\varphi$ in a Markov chain meets a given threshold $\prec p$, where $\prec$ is a comparison on reals and $p$ a probability. As for pLTL determining the emptiness of $V_{> 0}(\varphi)$ is undecidable, we consider several logic fragments. We consider parametric reachability properties, a sub-logic of pLTL restricted to next and $\Diamond_{\le x}$, parametric B\"uchi properties and finally, a maximal subclass of pLTL for which emptiness of $V_{> 0}(\varphi)$ is decidable.Comment: TCS Track B 201

A Full Non-Monotonic Transition System for Unrestricted Non-Projective Parsing

Restricted non-monotonicity has been shown beneficial for the projective arc-eager dependency parser in previous research, as posterior decisions can repair mistakes made in previous states due to the lack of information. In this paper, we propose a novel, fully non-monotonic transition system based on the non-projective Covington algorithm. As a non-monotonic system requires exploration of erroneous actions during the training process, we develop several non-monotonic variants of the recently defined dynamic oracle for the Covington parser, based on tight approximations of the loss. Experiments on datasets from the CoNLL-X and CoNLL-XI shared tasks show that a non-monotonic dynamic oracle outperforms the monotonic version in the majority of languages.Comment: 11 pages. Accepted for publication at ACL 201

Size versus truthfulness in the House Allocation problem

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomised mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomised mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of $\frac{e}{e-1}$. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of $\frac{18}{13}$ on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. In the case that the mechanism must additionally be non-bossy with an additional technical assumption, we show by utilising a result of Bade that an improved lower bound of $\frac{e}{e-1}$ holds. This lower bound is tight since RSDM for strict preference lists is non-bossy. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomised strategy of the administrator who interviews the applicants.Comment: To appear in Algorithmica (preliminary version appeared in the Proceedings of EC 2014

Digraph Complexity Measures and Applications in Formal Language Theory

We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this connection, and obtain several new algorithmic insights regarding both cycle rank and star height. Among other results, we show that computing the cycle rank is NP-complete, even for sparse digraphs of maximum outdegree 2. Notwithstanding, we provide both a polynomial-time approximation algorithm and an exponential-time exact algorithm for this problem. The former algorithm yields an O((log n)^(3/2))- approximation in polynomial time, whereas the latter yields the optimum solution, and runs in time and space O*(1.9129^n) on digraphs of maximum outdegree at most two. Regarding the star height problem, we identify a subclass of the regular languages for which we can precisely determine the computational complexity of the star height problem. Namely, the star height problem for bideterministic languages is NP-complete, and this holds already for binary alphabets. Then we translate the algorithmic results concerning cycle rank to the bideterministic star height problem, thus giving a polynomial-time approximation as well as a reasonably fast exact exponential algorithm for bideterministic star height.Comment: 19 pages, 1 figur