Related papers: Exponential-Time Approximation (Schemes) for Verte…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
Here, we give an algorithm for deciding if the nonnegative rank of a matrix $M$ of dimension $m \times n$ is at most $r$ which runs in time $(nm)^{O(r^2)}$. This is the first exact algorithm that runs in time singly-exponential in $r$. This…
We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. - We give a polynomial-time approximation scheme (PTAS) for a…
We study approximation algorithms for scheduling problems with the objective of minimizing total weighted completion time, under identical and related machine models with job precedence constraints. We give algorithms that improve upon many…
We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total…
In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are…
The max-cut problem is a classical graph theory problem which is NP-complete. The best polynomial time approximation scheme relies on \emph{semidefinite programming} (SDP). We study the conditions under which graphs of certain classes have…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…
Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee, Meeks and Pettersson (Stat. Comput. 2021) recently demonstrated that improved inference for areal unit count data can be achieved by…
A tournament is a directed graph T such that every pair of vertices are connected by an arc. A feedback vertex set is a set S of vertices in T such that T - S is acyclic. In this article we consider the Feedback Vertex Set problem in…
We consider a classical scheduling problem on $m$ identical machines. For an arbitrary constant $q>1$, the aim is to assign jobs to machines such that $\sum_{i=1}^m C_i^q$ is minimized, where $C_i$ is the total processing time of jobs…
We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in $\mathbb{R}^d$. In this setting, each vertex corresponds to a geometric object, and two…
We generalize the monotone local search approach of Fomin, Gaspers, Lokshtanov and Saurabh [J. ACM 2019], by establishing a connection between parameterized approximation and exponential-time approximation algorithms for monotone subset…
To analyze the worst-case running time of branching algorithms, the majority of work in exponential time algorithms focuses on designing complicated branching rules over developing better analysis methods for simple algorithms. In the…
We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…