The complexity of resolving conflicts on MAC

We consider the fundamental problem of multiple stations competing to transmit on a multiple access channel (MAC). We are given $n$ stations out of which at most $d$ are active and intend to transmit a message to other stations using MAC. All stations are assumed to be synchronized according to a time clock. If $l$ stations node transmit in the same round, then the MAC provides the feedback whether $l=0$, $l=2$ (collision occurred) or $l=1$. When $l=1$, then a single station is indeed able to successfully transmit a message, which is received by all other nodes. For the above problem the active stations have to schedule their transmissions so that they can singly, transmit their messages on MAC, based only on the feedback received from the MAC in previous round. For the above problem it was shown in [Greenberg, Winograd, {\em A Lower bound on the Time Needed in the Worst Case to Resolve Conflicts Deterministically in Multiple Access Channels}, Journal of ACM 1985] that every deterministic adaptive algorithm should take $\Omega(d (\lg n)/(\lg d))$ rounds in the worst case. The fastest known deterministic adaptive algorithm requires $O(d \lg n)$ rounds. The gap between the upper and lower bound is $O(\lg d)$ round. It is substantial for most values of $d$: When $d =$ constant and $d \in O(n^{\epsilon})$ (for any constant $\epsilon \leq 1$, the lower bound is respectively $O(\lg n)$ and O(n), which is trivial in both cases. Nevertheless, the above lower bound is interesting indeed when $d \in$ poly($\lg n$). In this work, we present a novel counting argument to prove a tight lower bound of $\Omega(d \lg n)$ rounds for all deterministic, adaptive algorithms, closing this long standing open question.}Comment: Xerox internal report 27th July; 7 page

Ethnicity - conflicts on land use - Sámi and Norse in Central Scandinavia in the Iron Age and the Middle Ages

publishedVersio

Labor Relations Conflict in the Workplace: Scale Development, Consequences and Solutions

Because the goals of employers and employees are often incompatible, conflicts are inevitable and an essential part of organizational life. The three studies reported in this paper addressed the issues of identifying the dimensions of workplace conflicts within organizations, exploring the consequences of conflicts, and finding appropriate methods of conflict resolution. The first study identified and developed three dimensions of labor relations conflict, including interest-based, rights-based, and emotion-based conflicts. The second study explored two sets of individual outcomes of labor relations conflicts and found labor relations conflicts had a negative effect on employee job satisfaction and affective commitment and positive effects on employee turnover intention and counterproductive work behavior. The third study tested the effectiveness of partnership practices as an alternative method of resolving labor relations conflicts. Suggestions are offered for future research on the labor relations conflict dimensions as well as its outcomes and solutions introduced in these studies