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Electronic Colloquium on Computational Complexity

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Reports tagged with Reductions:
TR96-043 | 16th August 1996
Edmund Ihler

On polynomial time approximation schemes and approximation preserving reductions

We show that a fully polynomial time approximation scheme given
for an optimization problem can always be simply modified to a
polynomial time algorithm solving the problem optimally if the
computation model is the deterministic Turing Machine or the
logarithmic cost RAM and ... more >>>

TR03-027 | 21st April 2003
Christian Glaßer, Alan L. Selman, Samik Sengupta

Reductions between Disjoint NP-Pairs

We prove that all of the following assertions are equivalent:
There is a many-one complete disjoint NP-pair;
there is a strongly many-one complete disjoint NP-pair;
there is a Turing complete disjoint NP-pair such that all reductions
are smart reductions;
there is a complete disjoint NP-pair for one-to-one, invertible ... more >>>

TR04-077 | 17th July 2004
Alina Beygelzimer, Varsha Dani, Tom Hayes, John Langford

Reductions Between Classification Tasks

There are two approaches to solving a new supervised learning task: either
analyze the task independently or reduce it to a task that has already
been thoroughly analyzed. This paper investigates the latter approach for
classification problems. In addition to obvious theoretical motivations,
there is fairly strong empirical evidence that ... more >>>

TR05-018 | 6th February 2005
Oded Goldreich

On Promise Problems (a survey in memory of Shimon Even [1935-2004])

The notion of promise problems was introduced and initially studied
by Even, Selman and Yacobi
(Information and Control, Vol.~61, pages 159-173, 1984).
In this article we survey some of the applications that this
notion has found in the twenty years that elapsed.
These include the notion ... more >>>

TR10-172 | 11th November 2010
Prasad Raghavendra, David Steurer, Madhur Tulsiani

Reductions Between Expansion Problems

The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of small sets in graphs. This hardness assumption is closely connected to the Unique Games Conjecture (Khot, STOC 2002). In particular, the Small-Set Expansion Hypothesis implies the Unique ... more >>>

TR14-164 | 30th November 2014
Cody Murray, Ryan Williams

On the (Non) NP-Hardness of Computing Circuit Complexity

The Minimum Circuit Size Problem (MCSP) is: given the truth table of a Boolean function $f$ and a size parameter $k$, is the circuit complexity of $f$ at most $k$? This is the definitive problem of circuit synthesis, and it has been studied since the 1950s. Unlike many problems of ... more >>>

TR18-173 | 17th October 2018
Eric Allender, Rahul Ilango, Neekon Vafa

The Non-Hardness of Approximating Circuit Size

Revisions: 1

The Minimum Circuit Size Problem (MCSP) has been the focus of intense study recently; MCSP is hard for SZK under rather powerful reductions, and is provably not hard under “local” reductions computable in TIME($n^{0.49}$). The question of whether MCSP is NP-hard (or indeed, hard even for small subclasses of P) ... more >>>

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