Swap Bribery

In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that the voter is asked to implement. Specifically, in our model the briber can change a voter's preference list by paying for a sequence of swaps of consecutive candidates. Each swap may have a different price; the price of a bribery is the sum of the prices of all swaps that it involves. We prove complexity results for this model, which we call swap bribery, for a broad class of election systems, including variants of approval and k-approval, Borda, Copeland, and maximin.Comment: 17 page

Parameterized Approximation Schemes using Graph Widths

Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability of a number of problems which are known to be hard to solve exactly when parameterized by treewidth or clique-width. Our main contribution is to present a natural randomized rounding technique that extends well-known ideas and can be used for both of these widths. Applying this very generic technique we obtain approximation schemes for a number of problems, evading both polynomial-time inapproximability and parameterized intractability bounds

Hitting forbidden subgraphs in graphs of bounded treewidth

We study the complexity of a generic hitting problem H-Subgraph Hitting, where given a fixed pattern graph $H$ and an input graph $G$, the task is to find a set $X \subseteq V(G)$ of minimum size that hits all subgraphs of $G$ isomorphic to $H$. In the colorful variant of the problem, each vertex of $G$ is precolored with some color from $V(H)$ and we require to hit only $H$-subgraphs with matching colors. Standard techniques shows that for every fixed $H$, the problem is fixed-parameter tractable parameterized by the treewidth of $G$; however, it is not clear how exactly the running time should depend on treewidth. For the colorful variant, we demonstrate matching upper and lower bounds showing that the dependence of the running time on treewidth of $G$ is tightly governed by $\mu(H)$, the maximum size of a minimal vertex separator in $H$. That is, we show for every fixed $H$ that, on a graph of treewidth $t$, the colorful problem can be solved in time $2^{\mathcal{O}(t^{\mu(H)})}\cdot|V(G)|$, but cannot be solved in time $2^{o(t^{\mu(H)})}\cdot |V(G)|^{O(1)}$, assuming the Exponential Time Hypothesis (ETH). Furthermore, we give some preliminary results showing that, in the absence of colors, the parameterized complexity landscape of H-Subgraph Hitting is much richer.Comment: A full version of a paper presented at MFCS 201

Parameterizing by the Number of Numbers

The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of numbers. Several classic numerical problems, such as Subset Sum, Partition, 3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with Target Sums, have multisets of integers as input. We initiate the study of parameterizing these problems by the number of distinct integers in the input. We rely on an FPT result for ILPF to show that all the above-mentioned problems are fixed-parameter tractable when parameterized in this way. In various applied settings, problem inputs often consist in part of multisets of integers or multisets of weighted objects (such as edges in a graph, or jobs to be scheduled). Such number-of-numbers parameterized problems often reduce to subproblems about transition systems of various kinds, parameterized by the size of the system description. We consider several core problems of this kind relevant to number-of-numbers parameterization. Our main hardness result considers the problem: given a non-deterministic Mealy machine M (a finite state automaton outputting a letter on each transition), an input word x, and a census requirement c for the output word specifying how many times each letter of the output alphabet should be written, decide whether there exists a computation of M reading x that outputs a word y that meets the requirement c. We show that this problem is hard for W[1]. If the question is whether there exists an input word x such that a computation of M on x outputs a word that meets c, the problem becomes fixed-parameter tractable

What Is an Act of Engagement? Between the Social, Collegial and Institutional Protocols

Engagement is not synonymous with commitment, even though both words are used in translations between English, French, and German. However, engagement is also not some supplementary phenomenon or a technical term that the phrase social acts already includes in itself or that the concepts of ‘commitment’ or ‘joint commitment’ somehow necessarily imply. In this article I would like to describe a special kind of social act and determine the function they have in relation between various agents. Most importantly, I would like to define their significance in the transformation of a group into an institution or higher order entity. My premise is that there are acts whose aim is to engage all others, since they refer to all of us together, and in so doing reduce negative (social) “acts” as well as various asocial behaviors within a group or institution. In this sense, engaged acts could alternatively also belong to a kind of institutional act, since they introduce certain adjustments to the institution, changing or modifying its rules, increasing its consistency and efficiency.First book series in Philosophy of the Social Sciences that specifically focuses on Philosophy of Sociality and Social Ontology. Studies in the Philosophy of Sociality Volume 1

(Total) Vector Domination for Graphs with Bounded Branchwidth

Given a graph $G=(V,E)$ of order $n$ and an $n$-dimensional non-negative vector $d=(d(1),d(2),\ldots,d(n))$, called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum $S\subseteq V$ such that every vertex $v$ in $V\setminus S$ (resp., in $V$) has at least $d(v)$ neighbors in $S$. The (total) vector domination is a generalization of many dominating set type problems, e.g., the dominating set problem, the $k$-tuple dominating set problem (this $k$ is different from the solution size), and so on, and its approximability and inapproximability have been studied under this general framework. In this paper, we show that a (total) vector domination of graphs with bounded branchwidth can be solved in polynomial time. This implies that the problem is polynomially solvable also for graphs with bounded treewidth. Consequently, the (total) vector domination problem for a planar graph is subexponential fixed-parameter tractable with respectto $k$, where $k$ is the size of solution.Comment: 16 page

Two-step closure of the Miocene Indian Ocean Gateway to the Mediterranean

The Tethys Ocean was compartmentalized into the Mediterranean Sea and Indian Ocean during the early Miocene, yet the exact nature and timing of this disconnection are not well understood. Here we present two new neodymium isotope records from isolated carbonate platforms on both sides of the closing seaway, Malta (outcrop sampling) and the Maldives (IODP Site U1468), to constrain the evolution of past water mass exchange between the present day Mediterranean Sea and Indian Ocean via the Mesopotamian Seaway. Combining these data with box modeling results indicates that water mass exchange was reduced by similar to 90% in a first step at ca. 20 Ma. The terminal closure of the seaway then coincided with the sea level drop caused by the onset of permanent glaciation of Antarctica at ca. 13.8 Ma. The termination of meridional water mass exchange through the Tethyan Seaway resulted in a global reorganization of currents, paved the way to the development of upwelling in the Arabian Sea and possibly led to a strengthening of South Asian Monsoon

Assessing the impact of diagenesis on foraminiferal geochemistry from a low latitude, shallow-water drift deposit

Due to their large heat and moisture storage capabilities, the tropics are fundamental in modulating both regional and global climate. Furthermore, their thermal response during past extreme warming periods, such as super interglacials, is not fully resolved. In this regard, we present high-resolution (analytical) foraminiferal geochemical (δ18O and Mg/Ca) records for the last 1800 kyr from the shallow (487 m) Inner Sea drift deposits of the Maldives archipelago in the equatorial Indian Ocean. Considering the diagenetic susceptibility of these proxies, in carbonate-rich environments, we assess the integrity of a suite of commonly used planktonic and benthic foraminifera geochemical datasets (Globigerinoides ruber (white), Globigerinita glutinata (with bulla), Pulleniatina obliquiloculata (with cortex) and Cibicides mabahethi) and their use for future paleoceanographic reconstructions. Using a combination of spot Secondary Ion Mass Spectrometer, Electron Probe Micro-Analyzer and Scanning Electron Microscope image data, it is evident that authigenic overgrowths are present on both the external and internal test (shell) surfaces, yet the degree down-core as well as the associated bias is shown to be variable across the investigated species and proxies. Given the elevated authigenic overgrowth Mg/Ca (∼12–22 mmol/mol) and δ18O values (closer to the benthic isotopic compositions) the whole-test planktonic G. ruber (w) geochemical records are notably impacted beyond ∼627.4 ka (24.7 mcd). Yet, considering the setting (i.e. bottom water location) for overgrowth formation, the benthic foraminifera δ18O record is markedly less impacted with only minor diagenetic bias beyond ∼790.0 ka (28.7 mcd). Even though only the top of the G. ruber (w) and C. mabahethi records (whole-test data) would be suitable for paleo-reconstructions of absolute values (i.e. sea surface temperature, salinity, seawater δ18O), the long-term cycles, while dampened, appear to be preserved. Furthermore, planktonic species with thicker-tests (i.e. P. obliquiloculata (w/c)) might be better suited, in comparison to thinner-test counter-parts (i.e. G. glutinata (w/b), G. ruber (w)), for traditional whole- test geochemical studies in shallow, carbonate-rich environments. A thicker test equates to a smaller overall bias from the authigenic overgrowth. Overall, if the diagenetic impact is constrained, as done in this study, these types of diagenetically altered geochemical records can still significantly contribute to studies relating to past tropical seawater temperatures, latitudinal scale ocean current shifts and South Asian Monsoon dynamics