Related papers: Statistical physics of hard combinatorial optimiza…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is…
In this letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This…
Survey propagation (SP) is an exciting new technique that has been remarkably successful at solving very large hard combinatorial problems, such as determining the satisfiability of Boolean formulas. In a promising attempt at understanding…
In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate…
We study the fundamental tradeoffs between computational tractability and statistical accuracy for a general family of hypothesis testing problems with combinatorial structures. Based upon an oracle model of computation, which captures the…
A high number of discrete optimization problems, including Vertex Cover, Set Cover or Feedback Vertex Set, can be unified into the class of covering problems. Several of them were shown to be inapproximable by deterministic algorithms. This…
The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization…
We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated…
Classical economics has developed an arsenal of methods, based on the idea of representative agents, to come up with precise numbers for next year's GDP, inflation and exchange rates, among (many) other things. Few, however, will disagree…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly…
Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in…
A feedback vertex set (FVS) of an undirected graph is a set of vertices that contains at least one vertex of each cycle of the graph. The feedback vertex set problem consists of constructing a FVS of size less than a certain given value.…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
Combinatorial algorithms are widely used for decision-making and knowledge discovery, and it is important to ensure that their output remains stable even when subjected to small perturbations in the input. Failure to do so can lead to…
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…
Real-world decision-making systems are often subject to uncertainties that have to be resolved through observational data. Therefore, we are frequently confronted with combinatorial optimization problems of which the objective function is…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…