hard drive – Partition limited and greyed out

I’m trying to partition my hard drive in order to install Ubuntu.
I’m using MacOS Catalina.
Upon selecting the device and clicking partition, I encounter that most of my hard drive space is greyed out with only 45GB to use out of 1TB. I certainly am not using most of it either. Please see image details below:

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How can I get over this and use more space for the partition? Appreciate any advice.

lvm create by sdc with no partition

I am new to linux, 🙂 and here is my question about lvm expand space.

I did couple time LVM space extension.
and on VM, I always expand the exist vm disk space, and then rescan the disk, and then create the new partition, and then create PV with the new partition and so on…..
the disk has partitions and which I can use the new space (extend) to create the new partition:
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BUT , NOW one of server shown:
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I expand the space from 100G to 130G, if I create the partition, I think the existing data will lost, how to expand LVM on this situation? thanks

Polynomial-Time Reduction: MakeSpan to Partition

Partition Problem:

Input: $A:=$ {$a_{1}, …, a_{n} $}. $a_{i} in mathbb{N}$ $forall i in$ {$1, …, n$}.

Question: Exists a subset $A_{1} subset A$ with: $sum_{a_{i} in A_{1}} a_{i} = sum_{a_{i} in Asetminus A_{1}} a_{i}$ ?

Output: Yes or No.

Makespan Problem:

Input: Jobs $J$ and $b in mathbb{N}$.

Question: Exists a Schedule $S$ with $FinishTime(S) leq b$ ?

Output: Yes or No.

So I have to change the Makespan Problem in a way that the Partition Problem gives me the correct answers for the Makespan Problem. $Partition leq_{p} Makespan$

First Problem: When the Makespan Problem has $m$ machines and not two, I don’t know how I can use Partition for that scenario. I could recursive iterate the jobs (so that I split Makespan in several Partition Problems) but then I had to use the Partition Problem several times and with my understanding, I am only allowed to change the Input for a Polynomial-Time Reduction.

But let’s say we have $m= 2$ machines. If Partition has the Output “Yes”, I know that there exists an optimal solution for the Makespan, so that I have an optimal Schedule with value= $dfrac{1}{m} cdot sum_{a_{i} in A}$. If $b leq dfrac{1}{m} cdot sum_{a_{i} in A}$, the result for Makespan is also Yes.

Second problem: But what happens if there is no optimal solution? I only receive “No” from Partition but I don’t know how bad the Partition result is.

I would be really happy if someone has an idea for this, I don’t know how to I could find a solution for this.

Thanks in advance!

Best Regards.

deployment – How to prevent Windows 10 feature updates from creating a recovery partition?

In our lab, we have a few dozens of dual-boot computers installed with Windows 10 and Ubuntu, using either legacy (CSM) or UEFI boot depending on the machine. In both cases, GRUB2 is used as a bootloader. All the machines have a custom partitioning scheme without a Windows recovery partition, as the latter is not needed. If a machine has issues, we rather reimage it from the network (using a PXE booted Linux).

Now the problem comes with Windows feature updates, the latest being version 2004. When one of these updates installs, it somewhat shrinks the Windows system partition to add back the recovery partition. Given its reduced size it would be fine to leave it alone, but this operation breaks GRUB as the Linux partition changes number, and the first stage of GRUB doesn’t understand partition labels to find its second stage (even on UEFI machines). If a machine is hanged on a GRUB rescue prompt, there’s no way to remotely correct the issue… sometimes leaving offline for hours (if not more) machines that must remain remotely accessible.

As we don’t have any use for the recovery partition, the question is how to prevent the updates from creating it in the first point? Of course we could have it there when imaging the machines, but given that we don’t actually want it, it seems just a waste of disk space.