[Lemon-user] Equality in MinCostFlows instead of LEQ and GEQ

[Dimitris Paraskevopoulos]

Many thanks, Alpár, really appreciated. I actually went through the network_simplex.h and I realised that, I also added an EQ option in the SuppyType enum, just to double check and yes you are right. 

Many thanks,

Dimitris

________________________________________
From: Alpár Jüttner <alpar.juttner at gmail.com> on behalf of Alpar Juttner <alpar at cs.elte.hu>
Sent: 01 April 2015 16:26
To: Dimitris Paraskevopoulos
Cc: lemon-user at lemon.cs.elte.hu
Subject: Re: [Lemon-user] Equality in MinCostFlows instead of LEQ and GEQ

Hi,

> I read in http://lemon.cs.elte.hu/pub/doc/1.2.3/a00005.html that :
> "The algorithms in LEMON support the general form, so if you need the
> equality form, you have to ensure this additional constraint
> manually."
> How can I do that manually? What does manually mean?

It you must ensure/check that the sum of sup(v) values for all nodes are
zero.

In case of the "equality form" the problem will infeasible is the
condition above does not hold. But if it holds, the equality, the LEQ
and the GEQ forms are all equivalent.

In other words, if you want to solve a problem using the equality form
and your input is meaningful, you can simply use either of the
inequality forms instead.

Regards,
Alpár