# On the Min-Max-Delay Problem: NP-completeness, Algorithm, and Int-Gap

@article{Liu2017OnTM, title={On the Min-Max-Delay Problem: NP-completeness, Algorithm, and Int-Gap}, author={Qingyu Liu and Lei Deng and Haibo Zeng and Minghua Chen}, journal={ArXiv}, year={2017}, volume={abs/1707.02650} }

We study a delay-sensitive information flow problem where a source streams information to a sink over a directed graph G(V,E) at a fixed rate R possibly using multiple paths to minimize the maximum end-to-end delay, denoted as the Min-Max-Delay problem. Transmission over an edge incurs a constant delay within the capacity. We prove that Min-Max-Delay is weakly NP-complete, and demonstrate that it becomes strongly NP-complete if we require integer flow solution. We propose an optimal pseudo…

## One Citation

### On the min-max-delay problem: NP-completeness, algorithm, and integrality gap

- Computer Science2017 IEEE Information Theory Workshop (ITW)
- 2017

It is proved that Min-Max-Delay is weakly NP-complete, and it is demonstrated that it becomes stronglyNP-complete if the authors require integer flow solution, and an optimal pseudo-polynomial time algorithm is proposed.

## References

SHOWING 1-10 OF 20 REFERENCES

### On the Quickest Flow Problem in Dynamic Networks - A Parametric Min-Cost Flow Approach

- Computer ScienceSODA
- 2015

This result shows for the first time that the quickest flow problem can be solved within the same time bound as one of the fastest algorithms for the min-cost flow problem.

### The quickest flow problem

- Mathematics, Computer ScienceZOR Methods Model. Oper. Res.
- 1993

It is shown that the quickest flow problem is closely related to the maximum dynamic flow problem and to linear fractional programming problems, and several polynomial algorithms and a stronglyPolynomial algorithm are developed.

### Fast, Fair, and Efficient Flows in Networks

- Computer ScienceOper. Res.
- 2007

It is shown that an s-t-flow that is optimal with respect to the average latency objective is near-optimal for the maximum latency objective, and it is close to being fair.

### Computational Complexity, Fairness, and the Price of Anarchy of the Maximum Latency Problem: Extended Abstract

- Computer ScienceIPCO
- 2004

It is shown that an s-t-flow that is optimal with respect to the average latency objective is near optimal for the maximum latency objective, and it is close to being fair.

### Max Flow and Min Cut with bounded-length paths: complexity, algorithms, and approximation

- Mathematics, Computer ScienceMath. Program.
- 2010

A primal–dual approximation algorithm is given for both problems whose approximation ratio attains the integrality gap, thereby showing that it is the best possible primal– dual approximation algorithm.

### Path Finding Methods for Linear Programming: Solving Linear Programs in Õ(vrank) Iterations and Faster Algorithms for Maximum Flow

- Computer Science2014 IEEE 55th Annual Symposium on Foundations of Computer Science
- 2014

A new algorithm for solving linear programs that requires only Õ(√rank(A)L) iterations where A is the constraint matrix of a linear program with m constraints, n variables, and bit complexity L is presented.

### Traffic Assignment with Maximum Delay Constraint in Stochastic Network

- Computer Science, Business2016 IEEE 83rd Vehicular Technology Conference (VTC Spring)
- 2016

This work looks into the traffic assignment problem in the stochastic network, considering the maximum delay constraint, and forms the Stochastic Delay Constrained Maximum Flow problem (SDCMF), and proves that it is NP- Complete.

### Constructing Maximal Dynamic Flows from Static Flows

- Mathematics
- 1958

A network, in which two integers tij the traversal time and cij the capacity are associated with each arc PiPj, is considered with respect to the following question. What is the maximal amount of…

### Sending Perishable Information: Coding Improves Delay-Constrained Throughput Even for Single Unicast

- Computer ScienceIEEE Transactions on Information Theory
- 2017

The first example showing that network coding can achieve strictly higher delay-constrained throughput than routing even for the single unicast setting is presented, and the NC gain can be arbitrarily close to 2 in some instances.

### Speeding-up linear programming using fast matrix multiplication

- Computer Science30th Annual Symposium on Foundations of Computer Science
- 1989

An algorithm for solving linear programming problems that requires O((m+n)/sup 1.5/nL) arithmetic operations in the worst case is presented, which improves on the best known time complexity for linear programming by about square root n.