Related papers: Complexity of Local Search for CSPs Parameterized …
The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and…
We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…
To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…
Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…
This article presents a discussion of optimization problems where the objective function f(x) has parameters that are constrained by some scaling, so that q(x) = constant, where this function q() involves a sum of the parameters, their…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:…
Local search is an effective method for solving large-scale combinatorial optimization problems, and it has made remarkable progress in recent years through several subtle mechanisms. In this paper, we found two ways to improve the local…
The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…
In a reconfiguration version of an optimization problem $\mathcal{Q}$ the input is an instance of $\mathcal{Q}$ and two feasible solutions $S$ and $T$. The objective is to determine whether there exists a step-by-step transformation between…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are…
Parameterized complexity attempts to give a more fine-grained analysis of the complexity of problems: instead of measuring the running time as a function of only the input size, we analyze the running time with respect to additional…
Constrained pathfinding is a well-studied, yet challenging network optimisation problem that can be seen in a broad range of real-world applications. Pathfinding with multiple resource limits, which is known as the Resource Constrained…
Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
Combinatorial optimization problems implicitly define fitness landscapes that combine the numeric structure of the 'fitness' function to be maximized with the combinatorial structure of which assignments are 'adjacent'. Local search starts…
In this paper, we consider lower bounds on the query complexity for testing CSPs in the bounded-degree model. First, for any ``symmetric'' predicate $P:{0,1}^{k} \to {0,1}$ except \equ where $k\geq 3$, we show that every (randomized)…
We consider an extension of the set covering problem (SCP) introducing (i)~multicover and (ii)~generalized upper bound (GUB)~constraints. For the conventional SCP, the pricing method has been introduced to reduce the size of instances, and…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…