Admins can filter entries by category in the CP, but I suspect that what you want is a secure way of allowing admins to only see their own categories.
I don't know of any native way to do this in the CP, and I am unaware of any addons that will do this. Have you done a search on devot-ee?
You may want to consider approaching this via the front end where you can use the channel tag in combination with the logged_in_user_id conditional, to only list entry titles filtered by that user ID and the user's assigned category or categories. Next to each listed title, a link to a channel edit form with the link passing the entry ID. The admin can then edit the entry status, or whatever else.
EDIT STARTS HERE
I will assume that you are using the channel form for the original entries, and either the author gets to set the category or you force the category via a hidden field and conditional depending on the author ID
For this to work, each target admin member group's settings must look like this:
Include Members in PUBLISH page multi-author list? = "yes";
Can access the control panel? = "yes";
Can access CONTENT section = "yes";
Can access CONTENT: Edit = "yes";
Can edit entries authored by others = "yes".
With that many (30) admins, your template code is going to be rather verbose, but let's see if you can live with that. You need at least two templates. One to list an admin's entries to be authorised and one for the channel form where the status can be changed:
Via whatever means, (access security is up to you) you will send your admins via the front end to a template as follows:
{if logged_in_group_id == admin_id_1}
{exp:channel_entries channel="whatever" status="pending" category= admin_id_1_category_id|another_admin_id_1_category_id}
{entry_title}<a href="{path='template_group/channel_form_template}/{channel_name}/{entry_id}">Authorize This</a>
{/exp:channel_entries}
{/if}
This is where it gets verbose - you need one of the above for each admin, plus a default to catch any non-admins that may turn up. Or you could use PHP in your template and set the category parameter dynamically according to the logged-in admin ID
Your channel form template looks something like this:
{exp:channel:form
channel="{segment_3}"
return="template_group/template/ENTRY_ID"
entry_id = "{segment_4}"
}
Content Label
Authorize Label
Submit
{/exp:channel_form}
I hesitate to mention this because it is overkill for what you want to do, but my HooBlong module has a feature that will allow you to filter inputs by category and member group, so you would not need a verbose entry listing template, and you would not need to keep updating the template if you ever needed to add/update member groups. See here.
Post your code if you need help debugging.