▁edges ▁of ▁a ▁wireless ▁communic ations ▁network ▁so ▁that ▁each ▁node ▁of ▁the ▁network ▁can ▁communicate ▁with ▁each ▁neighbor ing ▁node ▁without ▁inter ference . ▁Using ▁a ▁strong ▁edge ▁color ing ▁( and ▁using ▁two ▁time ▁sl ots ▁for ▁each ▁edge ▁color , ▁one ▁for ▁each ▁direction ) ▁would ▁solve ▁the ▁problem ▁but ▁might ▁use ▁more ▁time ▁sl ots ▁than ▁necessary . ▁Instead , ▁they ▁seek ▁a ▁color ing ▁of ▁the ▁directed ▁graph ▁formed ▁by ▁dou bling ▁each ▁und irect ed ▁edge ▁of ▁the ▁network , ▁with ▁the ▁property ▁that ▁each ▁directed ▁edge ▁ ▁has ▁a ▁different ▁color ▁from ▁the ▁edges ▁that ▁go ▁out ▁from ▁ ▁and ▁from ▁the ▁neighb ors ▁of ▁. ▁They ▁propose ▁a ▁he ur istic ▁for ▁this ▁problem ▁based ▁on ▁a ▁distributed ▁algorithm ▁for ▁- edge - color ing ▁together ▁with ▁a ▁post processing ▁phase ▁that ▁res ched ules ▁edges ▁that ▁might ▁inter f ere ▁with ▁each ▁other . ▁ ▁In ▁fi ber - opt ic ▁communication , ▁the ▁path ▁color ing ▁problem ▁is ▁the ▁problem ▁of ▁assigning ▁colors ▁( fre qu encies ▁of ▁light ) ▁to ▁pairs ▁of ▁nodes ▁that ▁wish ▁to ▁communicate ▁with ▁each ▁other , ▁and ▁paths ▁through ▁a ▁fi ber - opt ic ▁communic ations ▁network ▁for ▁each ▁pair , ▁subject ▁to ▁the ▁restriction ▁that ▁no ▁two ▁paths ▁that ▁share ▁a ▁segment ▁of ▁fi ber ▁use ▁the ▁same ▁frequency ▁as ▁each ▁other . ▁Path s ▁that ▁pass ▁through ▁the ▁same ▁communication ▁switch ▁but ▁not ▁through ▁any ▁segment ▁of ▁fi ber ▁are ▁allowed ▁to ▁use ▁the