Tomas Jirotka

The thesis summarizes known results in the field of NP search problems. We discuss the complexity of integer factoring in detail, and we propose new results which place the problem in known classes and aim to separate it from PLS in some sense. Furthermore, we define several new search problems.

more >>>Pavel Hubacek, Eylon Yogev

Local search proved to be an extremely useful tool when facing hard optimization problems (e.g. via the simplex algorithm, simulated annealing, or genetic algorithms). Although powerful, it has its limitations: there are functions for which exponentially many queries are needed to find a local optimum. In many contexts the optimization ... more >>>

Pavel Hubacek, Moni Naor, Eylon Yogev

The class TFNP is the search analog of NP with the additional guarantee that any instance has a solution. TFNP has attracted extensive attention due to its natural syntactic subclasses that capture the computational complexity of important search problems from algorithmic game theory, combinatorial optimization and computational topology. Thus, one ... more >>>

Ilan Komargodski, Moni Naor, Eylon Yogev

Ramsey theory assures us that in any graph there is a clique or independent set of a certain size, roughly logarithmic in the graph size. But how difficult is it to find the clique or independent set? If the graph is given explicitly, then it is possible to do so ... more >>>

Paul Goldberg, Christos Papadimitriou

The complexity class TFNP is the set of {\em total function} problems that belong to NP: every input has at least one output and outputs are easy to check for validity, but it may be hard to find an output. TFNP is not believed to have complete problems, but it ... more >>>

Alexandros Hollender, Paul Goldberg

The complexity class PPAD is usually defined in terms of the END-OF-LINE problem, in which we are given a concise representation of a large directed graph having indegree and outdegree at most 1, and a known source, and we seek some other degree-1 vertex. We show that variants where we ... more >>>

Arka Rai Choudhuri, Pavel Hubacek, Chethan Kamath, Krzysztof Pietrzak, Alon Rosen, Guy Rothblum

The Fiat-Shamir heuristic transforms a public-coin interactive proof into a non-interactive argument, by replacing the verifier with a cryptographic hash function that is applied to the protocolâ€™s transcript. Constructing hash functions for which this transformation is sound is a central and long-standing open question in cryptography.

We show that ... more >>>

Elazar Goldenberg, Karthik C. S.

In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products.

We say that an optimization problem $\Pi$ is direct product feasible if it is possible to efficiently aggregate any $k$ instances of $\Pi$ and form one large instance ...
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Robert Kleinberg, Daniel Mitropolsky, Christos Papadimitriou

We identify several genres of search problems beyond NP for which existence of solutions is guaranteed. One class that seems especially rich in such problems is PEPP (for "polynomial empty pigeonhole principle"), which includes problems related to existence theorems proved through the union bound, such as finding a bit string ... more >>>