Improved Parameterized Algorithms for Constraint Satisfaction

For many constraint satisfaction problems, the algorithm which chooses a random assignment achieves the best possible approximation ratio. For instance, a simple random assignment for {\sc Max-E3-Sat} allows 7/8-approximation and for every \eps >0 there is no polynomial-time (7/8+\eps)-approximation unless P=NP. Another example is the {\sc Permutation CSP} of bounded arity. Given the expected fraction $\rho$ of the constraints satisfied by a random assignment (i.e. permutation), there is no (\rho+\eps)-approximation algorithm for every \eps >0, assuming the Unique Games Conjecture (UGC). In this work, we consider the following parameterization of constraint satisfaction problems. Given a set of $m$ constraints of constant arity, can we satisfy at least $\rho m +k$ constraint, where $\rho$ is the expected fraction of constraints satisfied by a random assignment? {\sc Constraint Satisfaction Problems above Average} have been posed in different forms in the literature \cite{Niedermeier2006,MahajanRamanSikdar09}. We present a faster parameterized algorithm for deciding whether $m/2+k/2$ equations can be simultaneously satisfied over ${\mathbb F}_2$. As a consequence, we obtain $O(k)$-variable bikernels for {\sc boolean CSPs} of arity $c$ for every fixed $c$, and for {\sc permutation CSPs} of arity 3. This implies linear bikernels for many problems under the "above average" parameterization, such as {\sc Max-$c$-Sat}, {\sc Set-Splitting}, {\sc Betweenness} and {\sc Max Acyclic Subgraph}. As a result, all the parameterized problems we consider in this paper admit $2^{O(k)}$-time algorithms. We also obtain non-trivial hybrid algorithms for every Max $c$-CSP: for every instance $I$, we can either approximate $I$ beyond the random assignment threshold in polynomial time, or we can find an optimal solution to $I$ in subexponential time.Comment: A preliminary version of this paper has been accepted for IPEC 201

A polynomial kernel for Block Graph Deletion

In the Block Graph Deletion problem, we are given a graph $G$ on $n$ vertices and a positive integer $k$, and the objective is to check whether it is possible to delete at most $k$ vertices from $G$ to make it a block graph, i.e., a graph in which each block is a clique. In this paper, we obtain a kernel with $\mathcal{O}(k^{6})$ vertices for the Block Graph Deletion problem. This is a first step to investigate polynomial kernels for deletion problems into non-trivial classes of graphs of bounded rank-width, but unbounded tree-width. Our result also implies that Chordal Vertex Deletion admits a polynomial-size kernel on diamond-free graphs. For the kernelization and its analysis, we introduce the notion of `complete degree' of a vertex. We believe that the underlying idea can be potentially applied to other problems. We also prove that the Block Graph Deletion problem can be solved in time $10^{k}\cdot n^{\mathcal{O}(1)}$.Comment: 22 pages, 2 figures, An extended abstract appeared in IPEC201

Grundy Coloring & Friends, Half-Graphs, Bicliques

The first-fit coloring is a heuristic that assigns to each vertex, arriving in a specified order ?, the smallest available color. The problem Grundy Coloring asks how many colors are needed for the most adversarial vertex ordering ?, i.e., the maximum number of colors that the first-fit coloring requires over all possible vertex orderings. Since its inception by Grundy in 1939, Grundy Coloring has been examined for its structural and algorithmic aspects. A brute-force f(k)n^{2^{k-1}}-time algorithm for Grundy Coloring on general graphs is not difficult to obtain, where k is the number of colors required by the most adversarial vertex ordering. It was asked several times whether the dependency on k in the exponent of n can be avoided or reduced, and its answer seemed elusive until now. We prove that Grundy Coloring is W[1]-hard and the brute-force algorithm is essentially optimal under the Exponential Time Hypothesis, thus settling this question by the negative. The key ingredient in our W[1]-hardness proof is to use so-called half-graphs as a building block to transmit a color from one vertex to another. Leveraging the half-graphs, we also prove that b-Chromatic Core is W[1]-hard, whose parameterized complexity was posed as an open question by Panolan et al. [JCSS \u2717]. A natural follow-up question is, how the parameterized complexity changes in the absence of (large) half-graphs. We establish fixed-parameter tractability on K_{t,t}-free graphs for b-Chromatic Core and Partial Grundy Coloring, making a step toward answering this question. The key combinatorial lemma underlying the tractability result might be of independent interest

On Complexity of Minimum Leaf Out-branching Problem

Given a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in $D$ an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. Gutin, Razgon and Kim (2008) proved that MinLOB is polynomial time solvable for acyclic digraphs which are exactly the digraphs of directed path-width (DAG-width, directed tree-width, respectively) 0. We investigate how much one can extend this polynomiality result. We prove that already for digraphs of directed path-width (directed tree-width, DAG-width, respectively) 1, MinLOB is NP-hard. On the other hand, we show that for digraphs of restricted directed tree-width (directed path-width, DAG-width, respectively) and a fixed integer $k$, the problem of checking whether there is an out-branching with at most $k$ leaves is polynomial time solvable

Expanding the Usage of Renewable Energy Through Innovation and Technology Transfer

Moving green growth forward requires acknowledging the well-known carbon dilemma facing all nations: carbon-based economic development versus carbon emission reductions. Switching conventional carbon energy to renewable energy offers a potential win-win solution to tackle this dilemma. This dissertation empirically examines innovation and technology transfer of renewable energy technology at the international level with its three essays. The first essay explores how oil endowments of a country influence its innovation paths, specifically in the automobile sector. I show that a country\u27s oil endowment is a negative driver for alternative technologies, while a positive driver for oil extracting technologies. Depending on their levels of fossil fuel endowment, it appears that countries alter their domestic climate policy to either increase or decrease their dependence on fossil fuels. International climate policy could be designed to incentivize countries with increasing dependence on fossil fuels, and thus reach agreements for more rigorous action on climate change. However, in smaller developing economies with traditionally low capacity to innovate, technology diffusion is more important than technology innovation. Technology diffusion from wealthier nation to the world\u27s poorest is the fastest way to make the transition to renewable energy at the current state. Hence, the second essay shifts the focus to technology diffusion, exploring how foreign aid helps developing countries increase their capacity to use renewable energy technologies. I find that foreign aid on technical cooperation (transferring intangible knowledge) increases future renewable energy production more than foreign aid on non-technical cooperation. This opens a new window for the on-going discussion of program and policy evaluation in the field of foreign aid, while also contributing to the fields of policy evaluation and climate change policy, especially for the diffusion of renewable energy technologies. Having shown the effectiveness of foreign aid in the energy sector, the third essay explores whether aid allocation by bilateral donors responds to the recipient needs in the renewable energy sector. Bilateral donors have been known for allocating their financial assistance based on political interests among recipients such as former colonies and political allies. The recent trends show that they allocate aid aligning more to their commercial interest. The findings support the recent trends of following the donors\u27 commercial interest. Donors select recipients based on their economic interest especially through expanding their market having higher number of recipients. When allocating, physical proximity drives the amount allocated. This sheds some light on future research to explore the potential of multilateral agencies in allocating aid to meet the needs of the poor

Convention attendees\u27 attitude and its relation to intention

The purpose of this study is to assess convention attendees\u27 overall attitudes toward participating a convention and to examine how the attitudes are related to the attendees\u27 intention to participate in a convention in the future; The findings indicate that there is no significant linear relationship between the attendees\u27 attitude and their intention. In addition, attitude-intention relationship in respect to past participation, primary reason for participation, and residence is too weak to support the hypothesis; This study contributes to the convention marketing by measuring the convention attendees\u27 attitudes toward the attributes and identifying the most important evaluative criterion. This study also contributes to the existing knowledge in consumer behavior by providing empirical findings with regard to the attitude measurement and attitude-intention relationship